EDIT:
So, I ignored the first message and I got to the main menu. Realized all my saves were from .06 appearently, even though I was quite sure I played .07.
Anyway, I deleted the old saves as they were not compatible anyway. Started a new game with full experience. Skipped the introduction, and during the home-tour, another error came up, this time a shorter one.
So I deleted all old files and only extracted the new ones. It works now just fine, but it would be interesting what leads to the problem in the first place.
I usually always update renpy-games by just extracting the new files over the old ones, and in ~90% of the time, there is no problem with that.