Exactly the kind of situation that calls for careful outside-the-box thinking. He could attempt to use illusions to convince Luna that he won. He could summon an alien invasion to disrupt the game. He could angrily flip the chessboard and stomp away.
I feel the need to say that Loki hasn't actually lost this game yet. It is actually really hard to put a person into checkmate with just a knight and a king. Upon further thinking, I'm pretty sure it's impossible. At best, Luna can force the game into a draw. And before I get flamed, I feel the need to point out that I have nothing against Luna, I just want the sport of chess to be properly portrayed.
I concur with your statement on Loki's position. It is impossible for this game to have a winner. King/Knight and King/Bishop are the only two piece endgames that resolve without a victor regardless of how they are played.