Doesn't NVidia own a cloud-gaming company? Wouldn't this clause prevent another cloud-gaming company from springing up, and using consumer GeForce cards to power their servers? That's probably what this is all about.
I can't imagine that NV wants to force university students to have to buy Tesla cards, just to do their undergrad research projects.... or do they? :/
I think like you said, this is about Datacenters offering compute for cheap. Inference and training are in high demand, and renting server time, especially for grads just getting their feet wet, costs a lot less. What NVIDIA wants is these Datacenters using their suggested platform to deliver these services. Look at the Datacenter in Japan above. They're using a bunch of consumer GPUs, and then selling that compute capacity to customers. NVIDIA wants to make sure it's getting the correct cut of the pie. A GTX 1080 Ti goes for $800, a Quadro P6000 goes for $4,500, and a Tesla P40 goes for a whopping $8,000. With the standard code grads are putting together, there's almost no difference in compute performance (it's FP32). But NVIDIA wants customers making use of its FP16 throughput, which NVIDIA will be happy to remind you is massively gimped on its consumer cards.
Datacenter Service Providers will of course complain that people don't need all the FP16 or FP64 horsepower of a professional GPU, but their costs will extend massively. NVIDIA will then happily remind them of their GRID Virtual Workstation licensing, which will let them virtualize and distribute their Tesla horsepower to multiple users (for a per user fee of course).
Datacenters were trying to skirt the true costs of NVIDIA's training and inference ecosystem, and NVIDIA has fired back in a way that not only gives them way more money per chip produced, but also opens a gateway for them to license more software on an annual basis, further increasing revenue.
As others have said, NVIDIA is a machine. It has making money down to a science.