Linux always had software that has anti-cheat. First one I can think off that is both a native Linux application and has anti-cheat is Tibia. Aside from that is Valve. I am sure there are plenty of others too aside from those that opened up through Proton/Wine.

What we don’t have is kernel level anti-cheat and honestly I would rather stay away from games that deploy it than allow such software running in my computer.