Although this is true for most games it is worth noting that it isn't universally true. Usermode anti-cheat does sometimes work verbatim in Wine, and some anti-cheat software has Proton support, though not all developers elect to enable it.
Looking at you Rust.
Edit:
And the rest of you. If even Microsoft's Masterchief Collection supports it, I Don't understand why everyone else does not.
Then I saw the arewe…yet url and thought you meant Rust the programming language
Then I visited the arewe…yet link and realized it was the Rust game you meant after all