Are you writing in First Person or Third?
If you're writing in Third, you're a bit distanced from the action, and so you can, if you really REALLY need, go pull some tournament logs for an exciting and fun-looking chess match played by people of whatever ELO you need (Make sure you know what ELO you're going for - You probably aren't going to have your female lead be a 2700+ for example, but you probably want her to feel stronger than a 1600. Also do some research into what those ELO values mean. I just pulled from wikipedia, but I'm not writing a chess story :D), and appropriate that for the chess game between your MC and your Psychic Girl - Speaking of...
She's a psychic. Now, it sounds like she uses chess games very specifically to divine a person's potential future, but when most people hear psychic they think "mind reader" - If she is a mind reader, she either needs to not use the mind reading feature at all (may be difficult), or the MC has to be so amazingly scary that she can have full access to his mind and STILL lose (in which case HE would probably be about 2400 or so and she would have to be 1800 or some similar difference. Also he'd probably be super chess famous in that case).
You can include dialogue if you want, but if you're going to talk about the chess game directly, best find an actual chess expert to beta your story.
If you're writing in FIRST person, however- this becomes a lot more flipping challenging unless you yourself are horridly good at chess. If you're doing this in First Person, I'd honestly write it from your female lead's POV because that at least lets you use the magic system to cover for you not being amazing at chess yourself. If you don't care about how authentic the chess game itself looks, try getting yourself in the mood by playing someone who's horridly better than you, and recording every emotion you process, every moment of "WTF" - actually do that anyway, that'll help the characterization of it.
I'm interested in how this scene ends up being written :O Is this an ongoing series? and if so, where might I find it?
Edit to add: I'm not sure if I've ever seen a chess game written be strong just by being a chess game. However, you have this cool ability to tie it into, and you have characterisation you can write as a result of said Chess game so go for it!