A company that sells knives, and also invests heavily in restaurants, might be considered to be in the restaurant business, however

Nvidia spends a lot of money investing in downstream AI companies, in what feels like a rather incestuous circle

I'm not sure if this is what you mean too, but by the same logic it's not a 'graphics company' nor gaming etc. either. 'Chipmaker' as they say, specialising in highly parallel application-specific compute.

But it clearly does, as NVIDIA rolls out hardware and software optimised for deployment as AI compute.

You have a point. Then it's a "compute" company.