Well, no idea right now...
When you run with VMware, you run Windows. Crossover isn't windows, and you might have something in you virtual machine that isn't present in Crossover.
So first thing to figure this out would be to run a windows command and point it to your game's executable. In the debug options, you should ask for a log to be generated. In that log look for lines which complains about missing files, dll files in particular. Such files might point to what execution support software you're missing. If you want to post your log, please post it as "code" with the code button, and preferably only the parts the seem significant.
Off the top of my head, you might want to try and install ie7 in that bottle as that might get you going, but this is a wild guess on my part. I'm guessing that some web related piece of software is missing and that ie7 might just pull in what you need.
Lastly, I do want to help you, but I'm a Linux geek and don't own a Mac, so I can only go so far. Luck would have it that Crossover is sufficiently the same for Linux and Mac, from a user standpoint, for me to have at least a chance to help you.
Also, you might want to try a support ticket. If the staff can test the game, they might just try to figure things out for you, even if the game is officially unsupported.