yes the game does run on the remote desktop pc and essentially streams the video to the steam deck
I’ll admit the use cases can be limited, but if you want the ability to offload processing for graphically intense games it works well
my desktop is hard-wired into my network so I don’t have any lag when using remote play on my steam deck
I’m not sure if both machines were wireless how the performance might be impacted
It’s pretty easy assuming both of your devices are on the same network:
if you have a good home network it is pretty much indistinguishable from playing it directly on the deck
I can play Elden Ring with no video artifacts or noticeable input lag
here is a guide which has some screenshots
https://www.pcmag.com/how-to/remote-play-how-to-stream-games-from-your-pc-to-the-steam-deck