Ultimately the OS should be providing a service that can verify a program is running in a secure environment and hasn't been tampered with. That's something that's useful for things far beyond games. I kind of hope the cheaters win this war for now, to create the incentive for building a better, proper, standardized, cross-platform solution.
Having the kernel itself, actually deny any access... The game devs run a build without debug symbols (not that debugging could work with it on), and run with it... Also, this should severely limit what that process can do in terms of communication outside itself. And maybe a launch warning from the OS... "You are about to launch a sealed application that cannot be observed, do you want to continue? Y/N"
I think the more important question isn't how you implement an anti-cheat, it's why some types of games attract cheaters.
When victory in a game isn't about strategy but just about how quickly you can click o character's head, and just by doing it once you win the game, that makes the whole game a clear target for cheating. Everyone cheats as the sniper, nobody cheats as the medic.
I think you could make an FPS that cheaters hate by designing it so that it requires at least 2 players to defeat a player on the opposite team, e.g. by giving everyone weapons of different type and needing two types to defeat an enemy.
I wonder if anti-cheating game design is a thing?
Of course, I still remember seeing cheaters back then, in that game... usually quickly kicked off the server you were playing on.