Afaik for both Parsec and Moonlight the video is a capture of the screen encoded in h264 or h265 and streamed to the remote client. They may be based on RDP for input but I don't think that's the case.

Moonlight is open-source, you can see in the code yourself as I don't understand most of it. There is also a project that attempt to replace the associated Nvidia Gamestream server but it is quite basic and no longer maintained : https://github.com/loki-47-6F-64/sunshine