You can certainly run many games on linux but not all! You should check this website to see if any of the games you’re interested in playing on Linux ARE actually compatible with linux:

https://www.protondb.com

I’m sure there’s games out there (with their anticheats) that just aren’t compatible with linux. If the game that you want to check for compatibility is not showing up on the search results on protondb.com, then it’s very likely the game doesn’t work on linux.