I've been thinking of this post too much and I made a little continuation of it! Thought I could finish it earlier, but I was mistaken.
Basically Night gets extremely frustrated with his loss. And I mean how could he not? Him! Basically a god! Lost to some unintelligent mortal being! (From his perspective of course)
So he blames Killer for cheating. Even know he knows that the game was fair. He just needs someone to blame, to carry the loss of his mistakes. It doesn't apply only to games but also to his past too, where he blames Dream for not protecting or not caring enough for him. Or taking the attention and love he thinks he deserved away from him.
But the monologue he gave to Killer is not about his past or his view of the world. It's more about telling the Killer to know his place. Because for the time being he is a whipping boy for Night.
Killer understands. But just offers him another round. Which can be interpreted as him agreeing to Nightmare's terms or saying "fuck u, I can beat yo ass again". He holds the piece king in his hands, implying that even though Nightmare is strong, Killer still has some sort of power over him.
Nightmare knows he will most likely lose again. And yet he can't deny the offer. After all, Killer is an interesting fella to play chess with. (Or he eats the pieces. And then Killer catches him doing that he gently wipes his mouth with a napkin like "I have no idea what you are talking about")
Thank you @signanothername for inspiration! I really like how you view the characters and explain their dynamics between each other!
Credits:
Original idea belongs to signanothername
Killer belongs to rahafwabas
Nightmare belongs to Jokublog
OMG SO COOL?!
