There's a lot of software involved in GPUs, and NVIDIA's winning strategy has been that the software is great. They maintained a stable ecosystem across most of their consumer and workstation/server stack for many years before crypto, AI and GPU-focused HPC really blew up. AMD has generally better hardware but poor enough software that "fine wine" is a thing (ie the software takes many years post-hardware-launch to actually properly utilize the hardware). For example, they only recently got around to making AI libraries usable on the pre-covid 5700XT.
NVIDIA basically owns the market because of the stability of the CUDA ecosystem. So, I think it might be fair to call them an AI company, though I definitely wouldn't call them just a hardware maker.
As someone who codes in CUDA daily, putting out and maintaining so many different libraries implementing complex multi-stage GPU algorithms efficiently at many different levels of abstraction, without having a ton of edgecase bugs everywhere, alongside maintaining all of the tooling for debugging and profiling, and still having regular updates, is quite a bit beyond "barely passable". It's a feat only matched by a handful of other companies.
NVIDIA basically owns the market because of the stability of the CUDA ecosystem. So, I think it might be fair to call them an AI company, though I definitely wouldn't call them just a hardware maker.