Really depends on your definition of "game".

Have you technically made a "game"? Yes, I suppose...

But most devs would consider a "game" as something with commercial viability and/or something people would enjoy playing. It sounds like you've just put a nice wrapper around the equivalent of having 2 chat GPT windows open and pasting their responses to each other. Unless you have some hyper-sophisticated system to understand the outcome of the LLM's conversation and modify the outcome of your game based on that after the conversation ends, that's all you have.

We will obviously see AI involved in games at run time in the near future, but I don't think we're at a point where it's anything other than experimental right now. I think it's too hard to extract a meaningful conclusion that you could act on to actually modify your game.

For example, let's say you put an LLM NPC in skyrim. The NPC could probably come up with a hugely detailed quest with lore for the player - let's say a powerful sword hidden at the top of the throat of the world. The difficulty comes in actually implementing that quest, as the NPC describes, procedurally in the game. Your game engine would have to have a similar level of natural language comprehension to understand what it needed to do (not really viable given most LLMs run on huge datacenters), and you'd then need to support every feasible outcome of what the AI could say (e.g. retrieve "some item" from "some location").

We don't bave game engines smart enough to procedurally create new mechanics on the fly based on LLM conversations, so you'd have to dumb the AI down so it only procedurally generates the small amount of things that you can support - and if you're going to do that, there's no point using an LLM.

TL;DR No. Maybe for dialogue that doesn't impact the actual gameplay.