It looks like remote play is coming to PC and Mac officially. Shuhei Yoshida spoke through Twitter providing a most welcome response to the question.
By bringing PS4 remote play to PC, this would allow Sony to be on par with Microsoft, who has released the Xbox App for PC to allow users to stream their games to a PC.
Recently there was a developer who had his own app titled “Remote Play PC,” which costs $10 to support the developer.
Some people asked if we plan to provide Remote Play function to PC, and yes, we are indeed working on an official application for PC/Mac. 😀
— Shuhei ZERO HOUR (@yosp) November 27, 2015