Different operating systems have their own interfaces to allow user level programs (like games) to communicate with hardware. This is a great-over-simplification, but one OS may understand something like "drawTriangle(x, y, z)" while another may expect "drawPolygon([x, y, z])".

There are software projects to attempt to translate commands meant for one OS for a different OS (such as "Wine" or Valve's "Proton") and those work fairly well in cases that: 1) there's an analogous command, 2) the analogous commands have been accurately mapped, and 3) the analogous commands operate in user space.

That last point is the primary reason why, despite the best efforts of developers, some games still cannot work across OSs. Operating systems are built on top of different levels with the lowest being the "kernel" (of "kernel level anti-cheat" notoriety) and the highest being the user space (where you interact). Both Windows and Linux have these, but the boundaries around them, what they can and cannot do, and how to interact across those boundaries differs between each system.

So when a Windows game installs a driver to monitor everything that your computer does that driver (kernel level anti-cheat) is tailored very specifically to the extremely powerful, low level, and unique Windows kernel. Linux cannot run that natively. If the game pretends that spying on you is an essential component to launch then the game will not launch. If, however, a game is perfectly happy to just stay in user space where it belongs then it will probably work fine with the available translation layers.