You may not notice this, but streaming games has been around on mobile for some time. Moonlight is an open source app for iOS, Android, and Chrome that reverses Nvidia's GameStream feature and lets you stream games to virtually any device (instead of the officially supported Nvidia Shield).
An Nvidia is required card in your PC, but as long as you have that, you can stream games directly to your phone, tablet or even another PC. AMD has an official app for Radeon users named AMD Link.
With all these options, you have the choice: Steam Link works well and is platform independent, but does not have a lot of settings. Moonlight has many settings that you can customize to improve performance and control. (However, the rumble feature is not supported, as is the case with Steam Link.) AMD Link has some additional quality settings, but in my experience it is a bit more choppy.
I recommend starting with Steam Link. In my tests it was an incredibly smooth experience for most games, though some had some quirks (like a black screen). If you encounter problems or missing features, try Moonlight or AMD Link. Graphics and streaming were similar in my tests, but they depend heavily on your device and network quality.
Even if your network is relatively fast, streaming performance can be choppy or completely unusable ̵