"Should schools have a chess variant class where students invent and vibe code novel chess variants and play each other's variants?"

I don't know what you are saying. Sounds more like your objective is to have students brainstorm new ways to play chess. Why is there any indication that the LLM should assume this is a programming question?

In fact, it has divined that programming might be involved and offered that certain python libraries might be leveraged. You frame your input as a question about schools offering a certain class and the LLM responded by assuming that is what your objective was and started to help build such a curriculum.

Did you expect with your input that the LLM would simply jump into writing some kind of code? Should it have written a multi user chess playground? Should it have written a python chess variant? I personally think it did the reasonable thing and from the context you provided assumed your task was to build such a class pedagogically not produce some python code.

If you are focused on chatGPT lumping other forms of "hacking" or "cowboy coding" into the same bucket as "LLM Assist" and calling it all "Vibe Coding" I personally don't have an issue with that. They all fall into the bucket of fast and loose coding techniques. That is just my take on it though.