After trying to get this working and having only marginal success (Crossover 11.2.1 on Ubuntu 12.04.1 64bit--constant audio problems that are fixed by restarting, but often enough to be a pain, plus the controls continue to be recognized after you let up the key which makes movement difficult), I was looking for help.
I came across ResidualVM: http://residualvm.org/
This is an open source native implementation, for Linux, Mac, and Windows, of the actual underlying game engine behind Grim Fandango. You copy only the data files from the CDs to your disk then run the ResidualVM program, and voila! No need for any exe's, Wine, etc. Runs great in both 32bit and 64bit.
I've played well into Year 2 without a single glitch anywhere, using 3d Acceleration enabled (keyboard, no joystick). All sound, movement, etc. worked great.
Not sure how kosher it is to advocate other software here, but if you want to play Grim Fandango then ResidualVM is (IMO) much simpler to get going and seems to work better.
Still love my Crossover for other apps, but not needed anymore for Grim Fandango.
Cheers!