I don't quite understand what this project is. How does it work with Moonlight or is it a replacement for Moonlight? (The docs don't seem to explain why I'd want to use it.)
Moonlight is a client for Nvidia GameStream, a local streaming server solution. A computer running GeForce Experience hosts the GameStream server - a client device running Moonlight receives the stream.
Typically GameStream is only hosted from a computer running GeForce Experience, which I believe is Windows-only and only compatible with Nvidia graphics cards. This Sunshine project is an alternative GameStream server, so that it can be hosted on macOS and Linux as well.