The rider in question bought a Powertap hub. The option of doing the ramp test on a smart trainer was probably not common then. Today, I would suggest that newer riders should consider this, with some caveats. Riders who know they have high anaerobic power should consider doing the 20 minute test instead, but again with some caveats.
First, what's FTP?
As we increase our exercise intensity, the concentration of lactate or lactic acid in our blood rises. Below a certain threshold, lactate levels are stable as the body can process it (it's part of the aerobic energy cycle). Above it, they rise rapidly. You can't work sustainably above this threshold. It's often called maximal lactate steady state in some fields, and it may be more commonly known as the lactate threshold or lactate inflection point. FTP is the cycling power we produce at this threshold.
Now, we could directly measure your blood lactate levels in a lab, but this is inconvenient for practical purposes. All the duration-based tests are estimators of power at lactate threshold. This means that people think that on average, if you run the algorithm (e.g. 95% of your 20 min power in the 20 min test) you should get your FTP.
Andy Coggan and probably others once wrote that 60 minute power is your FTP. To be more precise, we should say that he thinks 60 min power is an estimator of FTP. It's since been shown that most people can hold FTP for 40 to 70 mins. Coggan may have been working with well-trained cyclists when he wrote that.
2 x 20 minute intervals at FTP is commonly suggested as a workout. It is actually a fairly challenging one. If FTP were actually equivalent to 60 min power, then why does 2 x 20 even exist? We would expect to see threshold interval designs like 5 x 15 mins - try to exceed 60 mins, just broken up into chunks.
Ramp test - no learning curve, less stress
In the ramp test, you pedal. The trainer increases the resistance every minute. You pedal until exhaustion. You take the power in the highest complete block, usually pro-rate the incomplete block, then take 75% of that as an FTP estimate. This may sound intimidating to new riders, but it is over pretty fast and you won't be that tired afterwards. The test feels easy, then the challenging section onsets quickly and the difficulty really ramps up. You aren't suffering for long.
If you Google, you should find that the ramp test is accurate enough for most cyclists. You should find that most cyclists' FTPs are 70-80% of their maximum power on the ramp test. Ramp tests use 75% as a default multiplier. Be aware that the ramp test is directly measuring your maximal aerobic power (MAP), i.e. at this power you're at or near VO2max (your aerobic energy system is at maximum output). We've essentially determined that most people have their threshold power at about 75% of MAP. (Added after R Chung comment.)
For beginners, you don't need to learn to pace your effort. You just go as hard as you can until you physically can't turn the pedals over. It's also relatively little stress on the body, i.e. you recover quickly and can get back to training. Pacing a 20 minute effort is not a trivial skill, especially when you have no reference point. Thus, I think that if you have access to a smart trainer, most people should start with the ramp test.
However, you want to see how you are doing in intervals based on that number. Riding at threshold should feel challenging but sustainable. Your heart rate should rise but hit a ceiling (e.g. I believe mine is 169-171 bpm, judging from observation). If you're really gasping for air and your heart rate keeps drifting higher, you may be riding above threshold. Training software has a bias adjuster, where you change the difficulty in 1 percentage point increments up or down. Feel free to use this if you can't maintain power. In particular, a minority of athletes might have the ramp test significantly underestimate or overestimate their threshold power.
TrainerRoad's default is the ramp test, and it can also adjust its estimate of your FTP based on your feedback after workouts (i.e. rate the workout difficulty). Wahoo SYSTM (formerly Sufferfest/SUF) recommends its 4 Dimensional Power test once a year, and it recommends its enhanced ramp test in the interim. So, in some sense, both these companies seem to be leaning towards the advantages of the ramp test. I am basically telling you to do what TrainerRoad does, just outside their system.
The ramp test will get you to near your maximum heart rate. I don't know if a subset of athletes may have medical contraindications that rule this test out. Obviously ask your cardiologist, but be aware that some might be unfairly biased against strenuous exercise.
20 minute test - cruel, brutal, possibly more accurate for some
In the proper version of the 20 min test, you warm up, then you do 5 minutes all out, then you rest 5 minutes. Then you do 20 minutes, and you take 95% of the average power as your FTP estimate.
The accepted answer casts the 5-min block as a hard warmup effort between threshold and VO2max power. This is actually not true. You are supposed to go as hard as you can. This is to deplete your anaerobic reserves. If you check the Zwift 20 minute FTP tests, you'll find that the 5 minute session is at something like 110% FTP, and you often get a 10-min rest before the 20-min effort. In my last 20 min test, my 5-min interval was a bit over 130% of my FTP estimate.
If you know you're good at anaerobic efforts, I think it's better to work up to the 20 min test. It should produce a more accurate FTP estimate. The alternative is to keep doing the ramp tests, adjust workouts based on intuition, and perhaps come up with a better multiplier for yourself (e.g. I think mine is probably 0.7 vs the default of 0.75).
The downside with the 20 min test is that 20 minutes after a 5 min effort sucks. It's about an hour long including warmup and cooldown. You need to learn to pace yourself. Having a previous accurate FTP estimate really helps with that, but it doesn't change the fact that the effort sucks. For beginners, there is a learning curve, meaning that your first few tests can give inaccurate estimates just because you're learning how to pace a 20 min hard effort.
The dual 8-min max efforts (FTP is 90% of the higher average power) is another test in this format. I think this protocol doesn't need you to deplete your anaerobic capacity. I am not sure how accurate it is.
The Wahoo 4DP test is even more awful than the 20 min FTP test, because it has an all-out 1 min effort at the end. It is available as a free workout on Wahoo's platform if you are so inclined. It will get you a sense of how well your power at various intervals compares to other riders. Of course, some of the power-duration models below can do the same.
Alternatives - power-duration models
Consider the concept of the power curve.
This is a graph of power on the y-axis versus duration on the x-axis. The above is my empirical power curve based on my efforts in the last 6 weeks - those have included an FTP test, so my 5 minute power is truly an estimate of my fresh max power. But I haven't sprinted, nor have I tried an hour-ish TT.
People have proposed mathematical models like the Critical Power model. If you get people to do 2-4 maximum efforts at certain durations, you should be able to mathematically estimate their theoretical power for any duration within a certain window (e.g. 1 min to 40 min). The Critical Power model is one of these. That model requires at least 2 max efforts when fresh, typically a 3-min and a 12-min one. Now, as duration goes to infinity, that model will say that your theoretical power goes towards an asymptote. That asymptote is known as critical power. It's usually pretty close to FTP.
Critical Power could be an alternative to FTP, but you would need some info on how to base threshold or sweet spot intervals off your critical power. The article did say you can take 94% of your critical power as an FTP estimate, although the percentage will vary individually. For VO2max intervals, I think the power target isn't as important as just going as hard as you can sustain.
There are other power-duration models with more parameters. I think a software called Xert has a proprietary one that purports to be able to just estimate your FTP as long as you've done a few max efforts in a certain range of durations.
Comments on the FTP formula
One answer mentioned a formula to estimate FTP based on age, weight, and gender. I'll argue that this is a poor choice. The formula is by Joe Friel and is as follows.
Step 1. Double your body
weight in pounds (1 kg = 2.2 lbs). Example: A body weight of 154 pounds (70 kg)
estimates an FTP of 308 watts (154 x 2 = 308).
Step 2. Subtract 0.5% for
every year beyond age 35. Example: If the above 154-pound rider is 50 years old...
Step 3. Women riders
can subtract 10% from the estimated FTP as found in steps 1 and 2 above. ...
First, if you run the math in step 1, you'll see that the formula estimates that a 35 year old man has a 4.4 W/kg FTP. That is very fit. That is comfortably in Zwift Cat A. That is probably well above the average fitness of US Cat 3 road racers. It isn't pro-quality, but 4.4 W/kg would tear it up on almost all group rides. The estimate for a 35-year old woman is 3.96 W/kg. This would have you tearing up most mixed-gender group rides.
Second, you could tweak the parameters in the formula to be more accurate. But even if you got better parameters, you are still left with an estimate of the average FTP given age, weight, and gender. Someone will come onto a forum and say my FTP is 100W above the formula! Another person will come and say I can't hold my formula power for 5 minutes!
Imagine a scenario where your FTP, or your max HR, or whatever is an important training parameter, and you can't estimate it easily, but you need a number right now. It is a perfectly sound strategy to plug the average in, provided the estimate is accurate (Friel's estimate is biased very high), until you have better data. If you know nothing at all, then you are more likely to be close to the average than you are to be far away from it. The problem is that you can estimate your FTP easily enough. If you needed an estimate right now, it would be better to ride to perceived exertion and get a ballpark from there. Also, as I mentioned, the ramp test is a pretty short test and it isn't very strenuous.
The lived experiences of ordinary cyclists on ramp tests
The analysis of lived experiences is important in some academic disciplines. It can help us understand social or cultural phenomena in more detail, e.g. the experience of illness.
That said, this part of the answer is less serious. I just wanted to show that beginners need not be afraid of the ramp test. So I checked YouTube to see if I could find videos of ordinary cyclists doing ramp tests. Not fit cyclists, and definitely not pros. If you peruse this section, remember that humans come in a range of shapes, sizes, and aerobic potential.
Benji Naesen is a cycling commenter on the Lantern Rouge podcast. He's relatively new to structured training. Without offense to him, he's closer to average person on the street in terms of fitness and he's also on the huskier side. For the sake of entertainment, he did his first ramp test, and then a few days later he did the 20 minute test. His assessment at the end of the video is that the 20 min test was a lot harder than the ramp test, and he also swore a lot more during the 20 min test. He got 198W on the ramp test and 190W on the 20 min test. That's a 4% difference, which is not huge. Moreover, check his average power during the 20 min test. He's doing negative splits (i.e. power declining through the test). If he had maintained an even pace in the 20 min test, his results would be even closer.
Here, Leonard Lee, an older cyclist who is also a bit on the heavier side, attempts his first ramp test. It was clearly effortful for him. But he persists.
Here, Ed Laverack's partner Charlie does a ramp test after not exercising for 8 months. She reflects on the experience afterward. Laverack is a former pro, but his partner is not.
Sam Flynn started a YT channel to chronicle her weight loss journey. Here, she also survives the experience, demonstrates improvement, and offers reflections.