Wouldnt your controller need to be in range of ps4?
Software probably sends the button presses to the PS4. The PC software asked me to connect my controller to PC via USB but thats as far as I've bothered to get.
Surely that'd end up with input lag?
Yeah if i remember right there was a bit of input lag when I played oddworld via remote play on my vita. It's not gonna be a perfect experience.
PS4 has had remote play since release I believe and theres an unofficial app out for android so you can stream to your phone. I assume it is the same basic method behind Steam TV but I'm not sure.
It might not be very good for fast paced games where reaction time matters but I could see myself making use of it from time to time.
Thinking about it I wonder how well a chromecast + unofficial remote play app would work. Could end up being a very cheap way to play on the spare telly.