I think the most stringent types of Windows anti-cheat rely on remote attestation of the operating system. It's theoretically possible to design a Linux-based OS that supports such a capability, but the sort of people who choose Linux are unlikely to accept a third party having the final say over their computer.

I, for one am disappointed that anyone has accepted it. Once it's widespread, service providers can demand it, as we're seeing with mobile banking apps and game anticheat.

I also strongly dislike requiring remote attestation for any kind of software I want to run. But what I also dislike is cheaters in my online games and I genuinely do not have a better suggestion on what to do.

Personally, I run Windows purely for gaming and don't let it near any important data. For the latter, I boot into Linux with separately encrypted disks.