It is an ego thing. Theo basically had Lucchino by the balls.
He got the money he wanted
He got the years he wanted
He got a little more power I'm sure
But Lucchino still had to show him who's boss. So he had the Globe run the story.
Theo was probably feeling a little unsure about the job anyway, but did battle and won his contract war - probably a little surprised by himself that he got everything he wanted.
Then once he realised Larry was going to start using the media on him, he just said screw it. He took the high road and left.