http://bugs.winehq.org/show_bug.cgi?id=30395
--- Comment #3 from Matteo Bruni matteo.mystral@gmail.com 2012-04-11 08:22:47 CDT --- I can't reproduce with the demo from http://www.fileplanet.com/44018/download/Carmageddon-TDR-2000-Demo, although it may not be representative of the full game. The demo does a system test on the first run, saving some stuff into the TDR2000.gfx and TDR2000.snd files in the game directory. Assuming the full game does the same, you could try to delete those files and start the launcher again, maybe the game at that point will adapt to the missing 24 bit texture format. Otherwise, you could just try to install the game in a new wine prefix.
If that doesn't help, I guess a +ddraw,+d3d_caps trace would be useful as a start.