I answer a little late (but as I just arrived on the forum then ...).
Unfortunately, Moonlight is only compatible with Nvidia cards. Parsec is the only viable solution for Radeon / AMD cards ownners.
About Parsec, I tested it under retropie: performances are bad and system updates can sometimes be problematic.
The best is to realize a dual boot "Retropie / Raspbian lite" with the raspbian only dedicated to Parsec (automatic launching at start, drivers for joysticks, Wake on LAN to computer, etc ...).
If some people are interested, I will offer a step-by-step guide for Parsec's friendly use (just give me a month to test my installation and find any problems