I hardly think he's singing if 'for' her, he wrote the song about her in the '80s. She was the 'uptown girl' in the music video as well.
He's married to another hot blonde that's 1/2 of Christie Brinkley's age (Alexis Roderick), so I doubt he's trying to get her back now.
I don't think he's trying to 'get her back.'
I think it was just about recognizing she was in the audience and the fact that it was about her.
If you watch the video, there's a certain 'interaction' between them.
When you said "Serenades Christie Brinkley" in the title, I thought that you meant he was singing 'to' her. I didn't see much of that in the video, all I could see was the back of his head, and a woman with blonde hair, I couldn't tell who it was.