This works because Apple is in the reversing arms race. Does it make sense for Dropbox to go down this path? Note that Google and your bank don't.
The problem is browsers just don't have a good standard way of accomplishing this.
It was extremely annoying. The last few times it happened I just didn't play for a while because I didn't want to bother with reauthenticating; that's when I realized that I didn't enjoy the game that much any more and cancelled my account.