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)
Videos, Saving/Loading, Starting a game
What does not
Nothing until now (about 1 hour of gameplay)
What was not tested
Playing through the whole game (but I'm at it ;-)
To get the videos to work do not install Xvid but ffdshow (see comment below) and then override avifil32. Videos will run very slow though (at about 1 to 2 fps). Some Nvidia drivers seem to have issues displaying the background. I use 169.12 and haven't had any problems.
Also some people reported that starting the game with "__GL_FORCE_INDIRECT=1 wine zak2.exe" seems to boost video frame rates.
Would be Gold status if videos would work without any problems.