Yeah PS Now is NOT backwards compatibility.
I have no idea why anyone thinks that it is. Backwards compatibility is the ability to play your existing legacy games on your new console locally. PS Now is a paid streaming service in which legacy games you may or may not already own are sent in a constant stream of data from a server on the internet at an additional cost to your ISP download cap every time you play. i.e. you are always downloading. Add to that the fact that most people don't have an internet service that runs at a constant speed which results in all sorts of problems.
Stick with local gaming. Streaming games is not ready for prime time.