I managed to play AVP2 on Linux without no problem
Here is what you should do to make it worked
1) Install it with cedega (no problem for me): cedega /mnt/cdrom/setup
2) cd where the game is installed
3) cedega avp2
4) choose the options what you want use to play
5) exit (do not start the real game)
To play really, now do
6) nice -n 19 cedega lithtech -cmdfile avp2cmdfile.txt +DisableLoadScreen 0
It would be interesting to manage to put this option in avp2cmdfile.txt, but I did not manage to do that.
7) GOOD GAME

I had no issue with this game

Joaopa