Would it be technically possible for these anti-cheat companies to make third party proprietary kernel modules I wonder, a bit like Nvidia does with their driver for example, and then require that to be installed and loaded to play? Although with the user able to make custom kernels that'd be a bit of a nightmare. Probably would have to be only supported with specific distro's kernels or something.

I agree with you and I wouldn't want to install that myself but just something I've thought about.