While Linux has not yet become a dominant gaming platform, you can still spend your time on plenty of games running on Red Hat Linux. Old UNIX games that have made their way to Linux include a variety of X Window-based games. There are card games, strategy games, and some action games.
On the commercial front, Civilization: Call to Power for Linux and Myth II are available to use on your Red Hat Linux system, but will soon disappear because Loki Software (which ported those applications to Linux) went out of business. The future of high-end Linux gaming might be in the hands of TransGaming Technologies, which has created WineX from current WINE technology to allow Windows games to run in Linux.
Commercial games that run natively in Linux are also available. These include games from id Software, such as Quake III Arena, Unreal Tournament, and Return to Castle Wolfenstein.