While Valve is mostly centered around supporting Ubuntu right now when it comes to their Linux initiatives, the Steam client and its games will generally work fine on other modern Linux distributions. For making it easier to run Steam on Fedora and Red Hat Enterprise Linux, the binary package has entered the third-party RPM Fusion repository.
RPM Fusion, the popular third-party repository for non-free packages and other out-of-tree RPMs that was a merger of Livna, FreshRPMs, and Dribble, now supports Steam. RPM Fusion supports Fedora 17, 18, 19, and Rawhide. On the RHEL side, Red Hat Enterprise Linux 5 and 6 are supported along with the EL derivatives like Scientific and CentOS. Thanks to community work, Steam can now be found for an easy RPM installation on these Linux operating systems.
For more details on fetching Steam from RPM Fusion, see this blog post
for instructions or visit RPMFusion.org