The key measurement for chainrings is the Bolt Circle Diameter (BCD). If you imagine those four bolts being points on the circumference of a circle, then the BCD is the circle's diameter. As always, Sheldon Brown's site is a good reference here (and his crib sheet will help you work out your bike's BCD).
So having found out your BCD, any shainring with that BCD, and with the same number of bolts, should fit onto your existing crankset.
Now, you also need to consider how wide the chainring is. If you imagine the chain going around the chainring during cycling, what you're looking for is to have a perfect fit as the chain feeds into the teeth.
The problem is that there are two common chain widths out there: 1/8" (generally used by track bikes, some fixies, bmx, probably others) and 3/32" (generally, any bike with a derailleur, including road bikes and mtbs). So when you're looking to buy a chainring, it will generally be spec'd either 1/8 or 3/32 to denote the chain that it is paired with. Without getting too bogged down in detail, the best combination is where both chain and chainring are matched, although you'll get away with a mismatch, as long as the chain is wider than the ring.
Now, you say that your BCD is 104, and point to a chainring that might be a good fit. Certainly the BCD is a match. Also, while that url doesn't say explicitly 1/8 or 3/32, it does say that the ring is compatible with 9/10/11 speed drivetrains. In other words, with a geared bike. So you can deduce that it is a 3/32 ring, and should therefore fit with your current chain.
Lastly, note that if you are going to fewer T, you may need to shorten the chain.