Answering to the question, I can say it's a big "if". Just selling badly on a gen won't necessary make a company quit. Sega didn't quit after Saturn, MS didn't quit after XBox, Ninty didn't quit after GC. I honestly thought they would do a phone/handheld hybrid again, but the rumour of the Xperia division sale really gave me some doubts.
In a way, I think they would quit: they are way more successful in home consoles and handhelds are a market that can die soon. But if they are trimming the company around the PS division, would it make sense if they trimmed an entire line of products in their core division? Would the Xperia sale mean that they will still make the phone hybrid but since PS division will make it they don't need Xperia.
I was betting on the phone hybrid because it could do some good numbers. Vita, troubled as it is, probably sold more than their last high-end phones did in the last 3 years combined. So it could go either way right now and we probably won't know before 2019/20.
Edit: my biggest concern with the "phone streaming" thing it that it doesn't look much feasible. It will only work on wi-fi. It won't work on the go with 4G connections. It's not video streaming where you have a buffer. And most people have data caps. I don't see the utility of having streaming if it will only work where you have wi-fi available.
