Additional aspect: I can't even start Plarium Play (desktop).
History: The game gave me the option to update, which I used. The game closed, and nothing else happened. After a few minutes I looked into Plarium Play, which just had the Launch button, no further indication about an update. I used that, the game started (or tried to - occasionally I have to close the game and start it again), and after a few tries it gave me the option to update. I tried this another time with the same result. After that I closed Plarium Play and restarted it (making sure there were no tasks running via task manager). Now it's stuck in the "MainWindow" (title of the task). I tried this several times now with the same result.
Edit:
Just a few minutes later, and everything works fine. After I once got a window with "Oops! Something went wrong." and a "Home" button that showed a HTTP-503 page for a split second and a few other restarts with the behaviour described above, Plarium Play started normally, required a new login (inconvenient, but definately acceptable :) ), made an update of the game and let it launch as usual. It keeps downloading something though, with slow progress.
It seems for with my approach it just takes a bit of time, or maybe some luck to contact the servers at the right moment. Hope this might help somebody.