What a unique take on the theme! I'm imagining how funny it would be for a segment like this to go in the middle of a cutscene in a AAA narrative driven game, like there's a serious moment followed by the combo bar and the handshake menu showing up.
It was a little hard to tell how exactly the handshakes were affecting my score, but I don't think that was the main focus point lol. It felt like the animations after each interaction got more dramatic as I got closer to clearing the room, and like there was some denser combos towards the end of the game. Very cool if that was the intent.