Some games with this on the store page run natively on Linux. Not sure how it works, does the Linux version just not use the anticheat?
They may be a native Linux-supported game.
Otherwise, I know Easy Anti-Cheat is available on Steam for Linux, you install it just like if it's its own game, then other games use it. I don't know about any other anti-cheat software.
You can always check out protondb.com for info on a specific game.