I'm not sure when it was enabled in the stable Steam client, but it looks like 5.1 sound is now enabled for Steam Home Streaming on Windows hosts and clients. I said last year that this was a big missing feature for the platform, so I'm glad they actually did it.
It wasn't a smooth process to get it working, though. Although everything looked like it was configured correctly, whenever I tried the streaming there was no sound. I eventually found this forum post which said that the old DirectX9 runtimes ("DirectX End-User Runtimes (June 2010)") are need on the client for it to work. After that, it worked fine. There was nothing in the Valve FAQs that I could find on the subject, so Valve really need to update their stuff to make it easier for users on this.
Also, it seems that Steam Home Streaming and Big Picture Mode is a bit buggy at the moment, too. That's disappointing, because Big Picture Mode really enhances the couch experience.
This 5.1 development now means that I can seriously consider purchasing games on Steam that I can play on the couch as well as on the PC. I'm thinking the upcoming No Man's Sky might be a perfect test of this.
Nevertheless, I might have a go at replaying Ori in the meantime.