.exe are DOS or Windows binaries. They are not compatible with Linux, which is a whole different operating system. There are some projects like Wine, which emulate a Windows environment under linux, and allow some Windows software to run under Linux. However, the applications that can run under Wine are limited.
To install games, you either get the precompiled package of the game for your version of Linux, or get the source code of the game and compile it yourself. Often, games have instructions on how to load them. You can get some more information about games under linux by searching google.
Totem is a front-end for Xine. You might want to look at the installation notes here for Fedora, for Xine and Totem.