Serviio

Would there be a way to get Serviio to play the sound already playing off the PC?

Jamcast service has that option but it's not free (has a 14 day trial if anyone wants to try it)

Should be able to use VLC to capture it and then pick up the audio stream from VLC.

Look at http://wiki.serviio.org/doku.php?id=stream_pc originally from viewtopic.php?f=3&t=1423&hilit=steam+desktop for how you steam the sound and video, and then cut it down to just sound. There may even be a post about audio only in that thread.