Try searching for a game using www.google.com/linux.
I did and one site it gave me was linux.tucows.com, which probably has many games. Unreal Tournament's site for linux is www.unrealtournament.com/linux.
If the games don't come in RPM format, then try installing them from the source code (usually packed into a tar/tar.gz/tar.bz2 archive). It is a bit tricky, but most of the archives contain README and INSTALL files which help (sometimes).
If the games are available as source code, then I dont see why one distro would be better than the other, unless maybe one distro has newer/more drivers for graphics cards.