The anti-cheats that the competitive games use rely on being able to trust that the checks they add to the kernel can't be overridden. It relies on Windows not being able to be modified to lie about that.
It's possible to change windows, just a lot harder. Unless you are talking about secure boot, but that's available to Linux just as much as to Windows.
It is about secure boot and TPM. Linux is unable to 'lie' well enough to emulate windows because it can't cryptographically verify that it is a legit windows install.
The anti cheat developers rely on Microsoft asserting that other cheats aren't loaded prior to the anti-cheat in the kernel. There is no such entity in Linux to attest that a particular linux install is not modified to load the cheats into the kernel before the anti-cheat.
Now, such an entity could be created, and a linux distro released that is signed by that entity, and then the anti-cheat could work on that distro. That would require you to only use that particular distro, though, and you would be limited in how you could change the kernel.
So far, there has not been the push needed to make that happen.
It would be virtually impossible to completely disguise the fact that you are on Linux. It’s hard enough to trick software in to thinking it’s not running in a VM.
Linux can lie about anything.