on fedora 20 under wine-1.7.30 (Compholio) it works flawlessly
just install via this command:
wine "/home/<user>/<pathtoinstaller>/setup_the_witcher_adventure_game_188.8.131.52.exe" /nogui
you will get a couple of error messages, but install process will be completed. then you can start the game by running:
/home/<user>/.wine/drive_c/GOG Games/The Witcher Adventure Game/TheWitcherAdventureGame.exe
An update to my previous post regarding the Galaxy Client. Went back and tried it again on a whim and there was a minor update downloaded and it then successfully came up with the id and password prompt to get initially connected. After that it downloaded an update to the game itself I believe and was able to launch. Still get the initial false crash notification from PlayOnLinux. It doesn't appear to successfully create/join the public lobby. It just sits there on Jolining lobby with the busy spinner going.