That fight is funny because it starts in the middle. If you look at the teaser -- there is a stray crewman in frame when the fight starts and even though the Captain is being attacked -- he just keeps on walking! LOL
He was all, "that Andorian has a knife -- I'm outta here!"
That guy didn't remain part of the "finest crew in Starfleet" much longer after that.
I was wrong it wasn't the teaser, but I found it on YouTube! Classic.
Cool! I can see why they edited the last part out of the final print because Kirk lifts his arm to press the intercom button and you can see his flabby stomach.