SpOck was not the best arc, truth be told it was Ock wank through and through always about how much better Ock was than Peter.
That said, the Norman figured out that it wasn't Peter and that he's technically "lost" to Ock, but Ock couldn't beat Norman.
After Peter got his body back that single line smacked was so "Peter" that Norman knew everything was back to normal.
The reveal was done in a single sentence and it was a perfect reminder of exactly how mutual the hate between Peter and Norman is.
One sentence was all it took for Norman to know Peter is back.
Looking forwards to the game myself as well anon.