The goal of kernel mode anticheat is to prevent other kernel-mode modules from tampering with the game's memory. This can kind of be done on Windows, as there's a pretty short list of kernel binaries, and all device drivers are signed.
This is out of the question on Linux, where there's probably 100,000 distro kernel binaries floating around, plus the ability to build your own with whatever modules you wish.
The only plausible solution is to force everyone to use the same kernel image. "To run Valorant, please apt install linux-vanguard-botnet-bin!"
Unfortunately this is a plausable enough outcome, and those games are so absurdly popular, that people will do it, especially given that having support for these games will likely drive new users to Linux.
If enough people do it, this opens the door for other software to latch onto it and start requiring a "verified kernel", so I'd rather just never see these games on Linux.
I think, it's not unreasonable to see basically a verifiable reference single-purpose gaming OS everyone has to use in competitive esports games. Steam and Linux are probably positioned well there.
Would be hilarious, if all gaming ultimately settles on a hardware independent console platform running on a locked-down linux! This would really please and piss off every faction at the same time. But honestly, not the worst compromise IMO.
We probably could run Linux distros under hypervisor (just like default Windows install those days runs not on bare metal, but under Hyper-V).
And then games that wish for anticheat start a separate VM in hypervisor with complete secure boot chain of trust. Would require GPUs to support SR-IOV though.