Here is my idea. Don't get too "chessy"...there are tons of readers out there who don't know anything about chess, and even the ones that do - they are not avid students. They wouldn't know the difference between 1.a3 and 1. Na3. So be light on the chess annotations.
Now, as you said, we are looking a bit into the psychology of the game, and I assume that since "he" is a professor and "she" is a student, you are wanting to put a bit of romance in there, eh? Be romantic - go King's Gambit...she cuts right for the heart with a Double Muzio, but at a critical moment when she has him by the throat, she throws the game away...or does she? Maybe it was a slip of the mind...or maybe she really likes him... Be interesting, without being too chessy. Speak of the theory without going too deep...maybe kind of like this (I'll let you write the story, of course, but here is a short bit of idea) -
She advanced her king pawn (description) and he advanced his king pawn forward two squares, eyeing her hands intently. As she gracefully reached for the king bishop pawn and slowly pushed it forward two squares, he eyed her with intrigue. "So, you're an aggressive player, eh?" She looked up and smiled. "From time to time."
(The game progresses - we see 1. e4 e5 2. f4 exf 3. Nf3 g5 4. Bc4 g4 5. 0-0!) He begins to think..."So, I guess you believe that knights aren't worth that much after all, eh?" "I wouldn't necessarily say that, Professor - sometimes I like to be the underdog - sometimes they have an uncanny ability to surprise you."
We proceed into the Muzio, and she is actually an expert, but she never let him know that. Of course, we failed to mention the teacher's pride - he has never yet lost to a student. Within a few moves, he is sweating, and works himself into a near-zugswang...and suddenly, mysteriously, she makes a terrible blunder...why? Well, that is for you to tell us why she made that blunder.
Ok, there's my idea. If you're gonna make a theme of a guy and a girl, it needs romantic features in it as well, not just chess analysis - people will be asleep. And if you want to feature a game, look up some old Chigorin games - I believe he was the first to really essay 0-0 in the Muzio.
I am collaborating on a novel with 2 other writers. We have a scene where a university professor plays chess with one of his students. He sort of "analyzes" her based on her method of play.
What I'm looking for is an unorthodox game but strongly played by both sides -- no glaring mistakes. It's probably better if the game is shorter too, not a 50 or 60-move game. I'm thinking 1. Na3 or Frankenstein-Dracula or Latvian Gambit, but keeping my options open.
Anyone willing to share one of their games for the book or have an appropriate game in mind?