I think you've misunderstood something here. No one charges fees for local streaming and doing so would likely be impossible. Sony and Nvidia charge fees to stream games from their remote servers not your local hardware
First off you're bring up an irrelevant semantics argument. Rainway doesn't just allow for streaming locally on your property, it allows you to stream from your pc to anywhere else on the world with viable connection.
As for the main issue Nvidia does charge for local streaming.
They have 2 wildly different services.
GEForce Now for the SHield
GEforce Now for Mac and PC.
GEForce Now for PC and MACs is the one where you strictly rely on a virtualized machine in the cloud.
If you want performance of 1060 that sets you back $20 for 20 hours. A 1080 costs $25 for 10 hours.
GeForce Now for SHield charges $8 a month but you don't get to select the hardware and it has conditions based on software and its usage. If you play an officially supported game at home you could stream with or without the subscription active. If you play an officially supported game away from home you will need your subscription to be active unless you are using a 3rd party service to get around it like Moonlight. If you play an unofficial game at home the subscription service is never invoked. If you play an unofficial game away from home you will need the subscription service unless you get a 3rd party app to get around Nvidia's controls.
It shouldn't be impossible for Nintendo to know what is installed on the machines they sell to us and block unauthorized downloads unless you have a very elegant hack that prevents them from knowing. Most people won't have that ability to do that or would care to try.