Linux and Windows/MacOS are two completely different operating systems. Programs written for one will not easily run on the other. However, there are emulators out there that will let you play certain games written for Windows (WINE) or DOS (DosEmu). Both are available from Debian. Be warned, though, that many newer games are very difficult to emulate, and may not work.
On the other hand, there are Linux versions of many popular games. We have Civilization/CivNet (freeciv), a real, free version of Quake, and more. Also, there are companies that have the rights to release Linux versions of certain games. Check out Loki Software.
Of course, if you're asking if Linux games (for Redhat/Mandrake/etc) will run on Debian without problems, then the answer is a 95% yes. The game will work, but it might not work out of the box.