No particular error shows up in the logs, the 360 is detected but not initialized as a gamepad though. Nothing comes to mind on what's going on.
You may want to post in the Steamlink forums (https://steamcommunity.com/app/353380/discussions/0/) and post the link to your log there also. If any of the controller works by itself, then it's not a config issue and usually in situation like this I'd check if there's enough power for both the WiFi and USB at the time, but since they already work (simultaneously) outside Steamlink that can't be it.
