Unfortunately not all developers export their games to Linux. However, Windows-only games can still be played in Linux if you copy the Linux binaries (libmono.so, ScreenSelector.so, LinuxPlayer) from the SDK version the game was built with into the right folders and rename LinuxPlayer properly.
I’ve just tested it with a free game which was released only for Windows and it worked fine on my 64 bit Ubuntu system. I assume the same can be done with OSX and Windows 64 bit binaries too.
The right SDK version can be obtained from the mainData file inside the *_Data directory. Just run head -c 30 mainData | strings
in a Unix shell or view the file in a hex editor or something similar.
Question: Is it possible for you to provide separate downloads for the runtime binaries? This would prevent me from downloading a >1 GB SDK setup if I need Linux binaries for a certain game.