The test results you have selected are very old and may not represent the current state of Wine.
Selected Test Results (selected in 'Test Results' table below)
Installation, configuration, videos, gameplay, keyboard controls all work. This test was run from a compiled 1.3.29 directory. The game was played on a notebook with a GeForce 8400M GS (driver version 270.41.06).
What does not
This game must be run from the installed directory. (A prefix and executable alone is not enough.) See comments below for a working example - especially if you receive a page fault when you try to start the game.
What was not tested
I played through the first chapter for this test.
Here's the terminal command that I used to run this test:
cd ~/.wine-demonstone/drive_c/Program\ Files/GOG.com/Demon\ Stone \
C:\\Program\ Files\\GOG.com\\Demon\ Stone\\demonlaunch.exe
I ran a test against 1.3.28 with the default settings (Particle Density/Gamme both middle, Shadows enabled, Advanced Graphics Effects enabled) in both fullscreen as well as emulating a virtual desktop of 1024x768.
I couldn't replicate the issues that you listed. All of the videos played fine and I didn't notice any problems with textures on the in-game models. I added five new screenshots to the gallery.
The problems that you mention (particularly about the textures) makes me think it might be related to your graphics driver. That's something to check at least.