Also, saying "the games just drop back to the desktop" isn't any help at all. What's happening is that they're printing an error message, but since you didn't start them from a command prompt, you aren't seeing that error.
Open up a terminal emulator (xterm, Eterm, aterm, konsole, gnome-terminal, any of these will work, and I've surely forgotten others that will also work), and run the game from there. ut2003 will start UT2k3, for example.
Then, when the game exits, post the error message (or just the full output) here.
Which glibc version do you have? Did you update glibc at all since installing? The problem referred to earlier was a problem with the U.S. boxed set of RH -- they shipped with a buggy C library (glibc) that causes problems with GL programs. The first version that works is noted somewhere in the README, in the FAQ section.
You should be able to rpm -qa | grep glibc to find out which version(s) you have.