I don't understand. What's an IIRC? And who's the current player? And how does other player needs to win it if it's the end of the round?
IIRC is If I Remember Correctly, but in this case I don't think he is.
It's not in the rules, so my ruling would be to let both players with no tricks score the cards in the Kings Trick. The player with the fewest points gets the Advantage card (if there is one). If players are still tied, the advantage card goes back in the pile and extends the game by one round.