X11 and Wayland are not the problem as those do indeed have stable binary interfaces.

Most games however need GPU access and that is only possible by either dynamically loading libraries or shipping the code for all the hardware you want to support with your binary (not an option).

That said, you don't really need a fully static binary but "just" target the oldest Glibc you want to support and minimize your imports as much as possible to avoid any unexpected compatibility problems. I put "just" in quotes because the toolchains on Linux don't make that easy if you also want modern programming language support, but it is viable.