Couple of things that mean the answer is no for now.

ChatGPT is trained on the world as we knew it at a point in time, why would you need all of that knowledge inside a game unless the game is set right now in the current world we live in? Those games would be pretty dull...

Dialogue choices are usually used to progress the story in one way or another, but there's no guarantee that the language model will say the right things or give you the right choices, so you might get stuck because the language model predicted the appropriate responses incorrectly, based on the way you phrased your questions.

ChatGPT has limited amount of context it can handle and so any lengthy dialogue leads it to start forgetting what you initially talked about which could get frustrating pretty quickly. Let me tell you, it's infuriating when you ask it to write code and it forgets your requirements as it gets halfway through the solution.

The compute power required is very high. Try running a local language model that is much smaller than chatGPT and you'll see it's not a natural pace of dialogue, so games would have to be constantly connected to the internet for dialogue to work. Fine in World of Warcraft, not fine in single player RPGs.

r u ok hun?

In fairness, every single time I've seen someone use grammarly they were extremely intelligent people with English as their second or third language. I also know one person who uses it because of dyslexia, which has nothing to do with intelligence. Be careful about shaming people for using software commonly used for accessibility.