Specifically:
Is it assured somehow that all versions of glibc 2.x are binary compatible?
If not, how can I run a binary (game) on my system which has been compiled for a different version? Can I install glibc in a different folder?
My specific problem is the compatibility between glibc 2.14 (what I have) and 2.15 (what the game wants).
I might also get a version for glibc 2.13 but I'm not sure if that will run on 2.14.
In general, running binaries that were compiled for an older glibc version (e.g. 2.13) will run fine on a system with a newer glibc (e.g. 2.14, like your system).
Running a binary that was built for a newer glibc (e.g. 2.15, like the one that fails) on a system with an older glibc will probably not work.
In short, glibc is backward-compatible, not forward-compatible.