Ah, darn. I wonder what's up with that, then...
So, you can't fork with cards that don't have any card on top. For example, if what they had in the picture was a spades of some kind, they wouldn't have a valid move because each one's alone or part of the beginning fork. That's pretty much what happen to me. For them, the place where they originally forked from, probably the 2 of clubs or 13 of clubs, can't be forked with again as a new move because they're behind a fork currently. So neither of us have any valid moves in either example, forcing us in this position.