Run it from the terminal as described here http://wiki.winehq.org/FAQ#get_log and post output. You probably missing 32-bit OpenGL library which is part of the video driver.
If you have an NVIDIA card, try to install the proprietary drivers and you will have great probability to get your game working.
An ATI Radeon HD series should work also, but it is less probable than an NVIDIA card.
The other video cards, probably will not work, since they don't care about good Linux support.