I don't really have well-thought solution, but more or less it's like this:
1) A single entity (with dictatorship rights) is designated to maintain core "system" in a way similar to how Linux kernel itself (or *BSD) is maintained. A new platform name is defined (or, ideally, "Linux" is redefined to mean kernel + core system).
2) Entity picks a set of core libraries which it is capable to actually maintain (and guarantee the backward compatibility for) and no compatible system is allowed to replace it/enhance/modify it in any way (even recompiling the kernel locally) without losing the (official) compatibility and ability to use platform name (which should be made a trademark).
3) Versioning policy is similar to Apple or Windows: every update (other than security fixes) should have a given name and version (with means to check that from code). The platform is updated in its entirety only, bugfixes are accumulated and introduced all at once.
I think that it is sufficient for the above set of libraries to include only functionality needed to write a game (generally speaking, any application with low-latency interactive video and audio).
In some ways it is similar to creating another distro dedicated to binary stability and binary multimedia applications, but it is not intended to be a full-blown distro with its own package management and policies, just a well-defined set of binary libraries + kernel.