I updated steam-link with the experimental packages. Before, I added the PR from @psyke83 in scriptmodules/ports/steamlink.sh.
Now, I was able to play the dolphin-emulator mith my xbox-360 controller:
I opened steam on the host-pc
I started steam-link in retropie
I switched on Settings/Streaming/Advanced Options/Start Streaming desktop and then I started
Now I was able to configure the controls within dolphin. I also made a combined hotkey to exit dolphin (In my case the Start and SELECT Button). Switched off Confirm On Stop and Render To Main Window on within the dolphin-emulator
Switched off Settings/Streaming/Advanced Options/Start Streaming desktop
Restarted steam-link and it worked
I also installed steam-devices on the Raspberry Pi too, but I don't know if it makes any differences. If I want to play a game with a keyboard, I have to plug off the controller before starting steam-link.
I'm running into a similar issue as well. Through searching through the moonlight github it seems the move to SDL2 has caused some issues with RetroPie. The developer of Moonlight has stated that they wont bother with fixing the problem as it comes from the way RetroPie handles controllers using SDL2 framework. Something around how the buttons are mapped and what the system sees. I'd love more help trying to track this down as well.