Intel Graphics Media Accelerator 900 with latest drivers.
It's enough to get me better graphics than this on other non-dreamcast games. Is dreamcast unique in this matter?
Even though the Intel GMA has DX9 features and is good enough for popular PC games to display the graphics more or less correct, the drivers probably aren't as good as ATi/NVIDIAs in general. From your shot, it looks like none of the textures have been loaded.
I don't think you do anything about this without getting a new card. Maybe try updating the drivers like you guys said. If that doesn't work you're out of luck.
P.S.: I must admit your screenshot looks pretty cool. It looks like flat shading.