I think it might be good for some games, but I still don't see it being too good for shooters, but that's alright.

I wonder if the controller will be available without the console, and if it will operate on non Steam games?

Probably, you can use the 360 controllers on virtually anything. It's just a matter of mapping the buttons and sticks. I've done it with my wired 360 controller using a software called Joy2Key.