I think sign up is more for keeping tack of your score, which is a good thing. They dont even ask for your email when you dont choose either FB or Google, that's the thing that caught my attention. Scores can really make it fun.
Okay, but instead of the popup asking to immediately log in, say "Congratulations on solving the puzzle. To keep your score, create an account (or log in with Facebook, etc). Otherwise, you can continue to play ... "
