After some digging I found the bug, where apparently Wine and ATI disagree on the behavior of some register, hilariously blaming each other. The even more hilarious fix is to set a flag in your x config. How an X driver setting affects a userland app is beyond me.
The net result of all this is of course screwing the user, with an impenetrable error message ("unhandled page fault") if you've got the unlucky hardware. I guess they landed a patch yesterday that at least identifies the problem and tells you about the above.