Wine will be unpredictable. You could try using the exact same version of wine used in Slackware and hope for the best.
Have you tried messing with all of the graphics settings in game? Decrease everything then re-enable one at a time? Sorry I can't be much more help, it's an old game and my memory is foggy.
I had next to no issues running the native Linux port of the game, but haven't run it for years now. The problems with that as I recall were getting it installed and configured in the first place. I used to disable all the movies - not worth all the trouble.
This person wrote a guide to getting the Linux port working:
https://gist.github.com/ubervison/1f...fca0bedaf5ad2d