Although the setup/options menu was okay, the game logos were UPSIDE DOWN and BACKWARDS, and that really weirded me out. Then the opening cutscenes were chopped up by black screens, gray screens and random logos. I created a log file which showed that my copy of AVP2 doesn't like fbo for the OffscreenRenderingMode.
Go to the 'run' command under programs, choose the bottle where you have AVP2 and run [regedit] (no brackets).
In regedit, go to:
hkey_current_user/software/wine
Right-click on the wine folder and create a key called [Direct3D] (no brackets). In Direct3D created a string called [OffscreenRenderingMode] (no brackets). I don't know if the capitalization makes a difference, but I do it that way anyway. Right click on your new string and select [modify]. Give the string the following value: [backbuffer] (no brackets).
The default is something called FBO. The log indicated that this program doesn't like FBO and even helpfully suggested backbuffer, so that's what I did.
My copy doesn't like fullscreen, but windowed mode now works for me.