I think Iglehart was out of breath because he was very nervous and also because the Radio City stage is extremely wide so he had to do a lot of running. Although I'm not his biggest fan, the number is much better in the show.
I guess Roundabout wanted to prove that the nominators made the right decision in feeling that Cabaret was just a recycling and left it out of Best Revival. They even recycled their Tony number.
"What was the name of that cheese that I like?"
"you can't run away forever...but there's nothing wrong with getting a good head start"
"well I hope and I pray, that maybe someday, you'll walk in the room with my heart"