There probably would to be a kernel API to check for anticheat measures. Even then, the OS being FOSS means that you can easily create rootkits, obviously. So secure boot etc will also be a requirement for Linux anticheat.

The real issue is devs not wanting to pay for hosting server side anticheat. I'd much rather have Valve convince them VAC is a good idea than to have them use intrusive anticheat measures or make Linux worse.