Sometimes it does. Sometimes it doesn’t.
The key word here is that while there are anticheats that work on Linux (Easy Anticheat, for example), they only work on a Native game. Steamdeck is using Proton to turn Windows games playable on the fly, but the Windows version of anticheat won’t work on Linux.
Furthermore, some companies just block Linux from being able to play them entirely. Destiny 2 is one. Roblox was another.