The Drama League is a bit different than the other awards-granting organizations, because the general public can be part of the Drama League. You just have to pay a membership fee. So you can get weird winners for Distinguished Performance, like Lin-Manuel Miranda for Hamilton. Miranda is an extremely gifted songwriter, but he did not even give one of the three best performances in Hamilton, let alone the entire season. (IMO, all three Tony winners for Hamilton gave better performances than Miranda did.)
I think Moulin Rouge and Danny Burstein had an advantage here, because Moulin Rouge has been running a long time, and probably a lot more people saw Moulin Rouge than any of the other nominated musicals, especially with the spring "catch-up" opportunity being unavailable this year. That being said, Burstein gave an award-worthy performance, and I'm very happy he won. It was going to be him, Christian Borle, or Adrienne Warren, and any of the three would have been worthy.
I found it interesting that someone said Burstein gives "boring" performances. I can see why someone would say that, because he's not that charismatic in general (he's probably the most charismatic I've ever seen him in Moulin Rouge). But I think that his "everyman" demeanor is part of what makes him a great actor. He's very natural in his performances. I would say the same thing about Norbert Leo Butz. They are not flashy, and their singing voices don't draw attention. But they are very believable as actors.
I'm a little surprised A Soldier's Play won over Betrayal, though.
"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"