From support:

The next release of Crossover Games will work out of the box with snow leopard. In the meantime there are some manual steps you'll need to do to get the current release running in snow leopard. These steps need to be done in Terminal.

So, first, you need to "thin" quartz-wm:

$ cd /usr/bin
$ sudo mv quartz-wm quartz-wm.bak
$ sudo lipo -thin i386 quartz-wm.bak -output quartz-wm

Then you'll need to launch CXGames from the command line with a special environment variable set which tells Perl to run as 32-bit:

VERSIONER_PERL_PREFER_32_BIT=yes /Applications/CrossOver\ Games.app/Contents/MacOS/CrossOver\ Games

Thanks,
Andrew