Nonprofit is a tax status, not a corporate structure.

It is in this case. After Musk invested in them, they’ve incorporated separate for-profit companies to essentially profit from the IP of the non profit.

No it’s not. It’s just a corporation with one kind of tax status owning another corporation with a different tax status.

Congratulations, you’ve just described a corporate structure.

It honestly doesn’t matter what the tax statuses of either of the corporations are. If Musk had invested in OpenAI with the goal of making tons of money off their IP (as opposed to wanting to open source it) and then the board decided to just hand over all the IP to another corporation essentially for free, Musk would be just as validated in suing.

You continue to miss the point. The term “non-profit” in no way describes this structure.

It's a structure in the sense of a non profit may not have shareholders or equity.

In a practical sense, there needs not be an operational difference, and is subject to scrutiny from the IRS to determine whether an organization is eligible non profit status