After seeing this post, I got my Link out and tried it. I initially didn't have sound either, but this comment on the bad site helped me resolve it. TLDR: re-installing the steam speaker driver thing.
Sometimes my pc gets confused on which sound output it's supposed to use. Have you tried alt-tabbing out of the game on your pc and setting the sound output to the steam link?
It's dumb, but sometimes windows refuses to acknowledge that audio can work if you don't have an audio device currently "active".
On my old computer I just plugged a headphone extender into the back and that fixed it, since it saw there was a connected audio device, even though there weren't even headphones attached.
I'm sure there was a better fix, but a cable on the back wasn't really bothersome.