Sunshine a host client for PC and Moonlight is the app for your phone that you'll use to connect it.
Whichever you use, you're just streaming the game from your PC to your phone.
Both let you use your phones touchscreen as a track pad to control the mouse, and there are various shortcuts for other function, like 3-finger-tap to bring up keyboard.
On that note, probably also a good idea to download the Hackers keyboard app if you go the sunshine route, since the native smartphone keyboard doesn't have things like Alt+Tab, F11, etc.
Edit: Sunshine/Moonlight also offer the benefit of being able to stream more mainstream games and use a controller that's connected to your phone, either via Bluetooth or USB.
No problem!
Final recommendation that just occurred to me, you'll want your PC hardwired to your router unless your WiFi is 5g+high upload speed.
Using 2.4g will be too unstable at anything but the lowest resolutions.
This also only applies to Sunshine/Moonlight.
Remote desktop isn't all that demanding, but there are no video quality settings or anything like that, and as mentioned before, it's not ideal for gaming, and frankly really doesn't work with games that require more than mouse input and an occasional key-press. Stormside would be okay, but GTAV, Minecraft, or any other "real" game would be nearly impossible to play with it.
