Some windows applications will work with a windows-compatibility layer under linux.
Look for the
Wine project. There is a special games-version in development called
WineX.
But there is no catch-all solution, generally windows applications will not run, (or run slower) under linux. Native applications are way better performance-wise.
File-extensions are handled differently under linux: they just
indicate the file type as an assistance. Executables do not need the .exe / .com etc file extensions. File-extensions work fine, but more as a convenience to the user, not the system.
(it has other means of determining executability)
Edited for formatting