Which SNES emu, and which controller?
A few emulators have this problem with Steam Link and Steams in-home streaming in general, some of them can be fixed by simply connecting a controller of the same type to the PC as the PC being streamed to, and some of them just can't be fixed. I know the Steam controller itself is one of the most common controllers that has issues being detected by emulators, because of the way it works. Assuming it's the one you're using, if you change the default behavior for the controller outside of games to the Game Controller option in the Steam Controller settings, it should be picked up by most emulators and should work fine. But again, that depends on the emulator.