Linux

Ah, so they don't actually say that they read kernel space. They check the version of all installed packages and checksum the installed DLLs/SOs.

If the user still has root privileges, this may still not prevent sideloading of kernel modules. Even if it would detect a kernel module that has been sideloaded, I believe it's possible to write a kernel module that will still be resident after you unload it. This kernel module can then basically do anything without the knowledge of userspace. It could for example easily replace any code running in userspace, and their anticheat would miss that as it doesn't actually check what code is currently running. Most simply, code could be injected that skips the anticheat.

Of course, in their model, if a user isn't given root privileges it seems much harder to do anything, then probably the first thing you'd want to look for is a privilege escalation attack to obtain root privileges. This might not be that hard if they for example run Xorg as it isn't known to be the most secure - there's a reason there's a strong recommendation to not run any graphical UI on servers.

Another way if you don't have root is to simply run the code on a system that does but that does have such a kernel module - or perhaps modify the binary itself to skip the anticheat. I don't see anything preventing that in their scheme.