To get one of the MDisks that contains a bonus game you need to register on the official site, enter your save game code and complete a "mission" - some kind of word minigame. The registration and code entry seem to be working still, however the mission window is not working - it only displays "back" and "homepage" buttons. I wonder if GOG can ask UBISOFT to fix the homepage and if not if there is a way to get the safe unlock code without doing the mission (it actually changes depending on your savegame statistics).

Have you got up to the final save point in the game? I tried to log onto the site earlier and got the same problem as you (non GOG version), but now that I'm at the end it works fine.
Doesn't mean it makes any damn sense though. The mission on the site is weird, man.