Game developers can ship an attested runtime (or hell, even an attested kernel) with the game and, refuse booting it unless the kernel passes some boot tests. Most Linux games already containerize their runtime anyways.

Locking down Linux totally is impossible, but the same very obviously goes for Windows and even macOS as well. Locking down a Linux runtime well enough to play online games seems trivial in my opinion. It's just a lot of work that would be better-spent preventing Windows hackers from pants-on-head insane DMA exploits.