I just successfully played through the entire game with Wine. I used the version of the game I purchased from the Amanita Design website (through the Humble Bundle store). I installed Wine 1.9.16 (the latest development version, packaged for Ubuntu in the Wine Builds PPA:
https://launchpad.net/~wine/+archive/ubuntu/wine-builds).
Wine 1.8.x is also reported to work:
https://appdb.winehq.org/objectManager.php?sClass=application&iId=17463Issues: sometimes the animations were a little jerky, and on the save game screen previews of the saved slots were not visible until I exited and re-entered the game.