WINE Is Not an Emulator (that's what the acronym actually stands for).
At a program level, WINE creates a dummy Windows directory structure, slaps files where an exe expects them, and executes the program.
EXEs (well, all programs) will use system calls to request resources (ie. files, access to hardware like GPUs, data from other processes) which Windows maps to certain areas of memory and has its own protocols for how to handle requests. Linux has its own protocols and methods that are incompatible, hence why Windows and Linux apps can't run natively together.
Then the magic happens: WINE maps these requests to Linux requests so that the running program is none the wiser. It asks for GPU resources like a Windows app would, then gets those resources back just like a Windows app would expect. There are thousands of edge cases, hundreds of system calls, and a bunch else that complicates things but that's how WINE (and Proton) works.
The reason this fucks up Kernel-level anticheat is that it isn't trying to communicate via these established channels. They usually operate with full resources outside of the jurisdiction of your OS, and scan your memory bit-by-bit rather than asking the OS politely via system calls for info on other processes.
With WINE, whilst a typical application will not notice the differences they're designed to not throw a fit if your underlying OS is configured differently, a kernel anticheat will not even recognise the system as a valid OS even if it was able to run in the first place.
The solution here is systems like EasyAC that give up the benefits of being able to analyse processes at the kernel level in favour of portability. Another potential solution (though unlikely imo) is a cross-platform kernel anticheat protocol, that all major operating systems agree to implement, similar to how operating systems will implement the TCP/IP protocol to communicate across networks regardless of underlying OS.
Now the reason "WINE"s acronym is particularly important is that if it DID emulate windows, as in what most virtual machine providers do, then anticheat would be running in an environment mapped out like a real Windows install - because it is. This is how many Linux gamers prefer to run certain titles, and something that should always be functional. It is much more annoying to maintain, However - balance how much you really wanna play the latest COD with your willingness to debug GPU passthrough shit.