In addition to Nathan's answer, you could run a 10-speed chain on the R8000 crankset. It would probably work fine, depending on the specifics of your bike and what else you may be changing - such as replacing the original 53/39 standard crankset (if that's what it is) with a 50/34 compact R8000 crankset.
It might not shift as well, and the wider 10-speed chain might have a tendency to drop inside the crankset when shifting to the small chainring. And you might need to adjust your front derailleur.
Or it might work fine with no changes needed at all.
And there's a small chance it won't work well at all. The derailleur might always throw the chain totally outside the entire crankset every time you try to shift to the outer chainring.
Shimano's specifications are usually extremely conservative. If Shimano's specifications say two parts are compatible, they will work together and they will work well together. But you can usually go a bit outside the specifications and compatibility charts for some things, like using a 30t rear cassette even though your rear derailleur can only officially handle a 28t cassette. *
The slight difference in width between a 10-speed and 11-speed chain and how it will shift on the crankset falls into this category - you can go a bit outside what Shimano says will work and probably get perfectly acceptable results. There's a decent tolerance in the width of the front derailleur cage, and the chain width is close enough that any difference in chainring spacing likely won't cause too much if any problems. You may have to add a chain catcher to stop the chain from falling inside the small chainring on downshifts. (This bit of leeway does not apply on the rear, though - a 10-speed chain on an 11-speed cassette isn't going to work well if it works at all, and as Nathan noted an 11-speed chain on a 10-speed cassette will have shifting issues.)
* - except for shifter and derailleur pull ratios. The only "non-compatible" combination there that I'm aware of that works is older 10-speed shifters (and lower) such as 6700 or so can work with 9-speed MTB rear derailleurs.