Actually it seems to be the bug in the Unity engine - it's not that obvious but the engine expects to see a directory AppData\LocalLow in the user profile and fails to create it (maybe it's there in recent WIndows versions but, well, last version I used extensively were Win2k and I don't remember it there and Wine does not create it either).
The fix is trivial: in your WINEPREFIX create drive_c/users/YOURUSERNAME/AppData/LocalLow/ (do not forget to replace YOURUSERNAME with the actual login).
Same fix works for, eg, Larry Reloaded - a FAQ maybe?
PS Played through Episode 1 with wine 1.6 plus this fix, everything seems to work except that the game is incredibly slow at times, usually while plotting path for the character to walk (still quite playable, and re-starting the game seems to fix this to some extent). Episode 2 works even a bit better - no slow path calculations at least.
UPDATE: Played through the whole 4 episodes, no major problems, just a minor graphics glitches - sometimes the character is painted on top of the objects in front of her, probably engine's fault, and sometimes the shadows are flickering like mad - a bit less with "Fastest" graphics setting. Wine 1.6, GeForce GT640, Slackware 13.37.
Post edited December 04, 2013 by jmcl