It's a technique that can be used to help a male singer find the right placement for bright and forward singing. He may have been having trouble finding his place of resonance for this particularly bright/high moment! I also noticed he made it an acting choice for a few moments... He sounds fantastic either way - He's a real talent, we need more of him! Message him on IG and ask - he might answer the question himself!
He is fantastic, in both voice and acting. But drawing attention to the former where he is inhaling through the nose, it is a bit distracting. Such a great voice and performance though. Seeing that clip also reminds though how truly awesome Donna was in the role. Bette is good, but Murphy just hit it out of the park for me.