Hmmm...something tells me the prince really wasn't with the heroine and some fate/god/etc.....is making a double of the prince in order to push the "game plot" forward.
I mean, I find it seriously suspect that she just HAPPEN to see the prince on a date with heroine, in the same manner as the game, right when she decides to leave the house.
Plus, that totally mismatches how he acts and thinks even when he's not around her.