To be fair, you can also do that on PC using Steam Play or other similar services.

I actually had no idea that existed. Can you pause a game on your PC and resume it on your phone? Or what mobile hardware does it use?

It streams from your PC, so you need your PC online at all times, your phone online, and a good connection between the both of them.

I've done it on the ps4 to my android phone. It was pretty neat playing bloodborne with an 8bitdo sn30.

How'd you get Remote Play working with a 3rd party controller? I thought it only worked with a Dual shock 4.

I used chiaki. It works with any controller connected to your phone or even a built in touch control system that probably would suck to use, though i did need it for the home button and did have to remap controls bound to the touch pad buttons. We were even able to play borderlands on local coop that way despite only owning one dualshock 4.