Doesn't Kairi technically count as a princess? I mean, she has her prince(sora) and she has a good friend(selphie/riku) shes also a princess of light. And there's also the fact that Disney worked to help make the game.

Yes, she's a princess from Disney merchandise. But she's not a princess like Belle, Snow White au Cinderella, etc etc. Disney doesn't even have most of the rights to Kairi, Squaresoft originally came up with this character, so it's actually a Squaresoft character. But she's a princess, and nonetheless partly a Disney character.

I would say no because she's from a video game, not a movie. All of the official princesses were in sinema first.

I count Kairi as a princess. But not an official Disney Princess, considering Disney never crowned her one, and plus she's only in a video game, and not a movie, (she was created in a video game).