Anti-cheat software are tools designed to prevent cheating in games. Anti-cheat software typically prevents games from running on Linux, since these anti-cheats don't have Linux support integrated. However, more games with anti-cheat are now becoming playable on Linux.
Anti-cheat games with Linux support
You can see which games have support here.
Details of Anti-cheat Linux support
The most popular anti-cheat software are Easy Anti-Cheat, BattleEye, and VAC. VAC natively supports Linux. Moreover, the anti-cheats EasyAntiCheat and BattleEye currently have support for Linux through Proton. This has resulted in some games enabling this Proton support, so that they're playable on Linux.
Easy Anti-Cheat became supported in late 2021 through a recent Epic Online Services Easy Anti-Cheat software development kit (SDK). Since many Easy Anti-Cheat games don't use the Epic Online Services version of Easy Anti-Cheat, these games must update or change out their SDK for the ability to enable Proton support. This means it's likely that many Easy Anti-Cheat games will not support Linux for a substantial amount of time.
BattleEye Proton support became supported in late 2021. Developers can enable Proton support for their game by emailing BattleEye developers.