Aren't Linux syscalls backward-compatible? So can't you just static-link your own libc clone (like MUSL or whatever)? (Can't staticaly-link normal libc due to licensing, IIRC)
By using MUSL it is possible to build fully statically linked applications that works everywhere, however dlopen(), dlclose() calls, that are used for loading shared libraries and plugin at runtime on Unix-like systems, do not work with MUSL.
The bigger problem is that glibc cannot be statically linked properly. It dlopen's some libraries, like for NSS. Maybe games could avoid triggering those cases but musl is definitely better.
While syscalls themselves are backward-compatible (even for faulty behavior), I think I've read somewhere that some parts of DRI are not, but I've lost the source on that.