Grant:
Is there a way to digitally send all audio output from one computer to
another where it will then be sent to the sound card for actual
playback? Maybe jack? Could the two computers be connected via some
type of direct cable method instead of going over a local network?
Yes, its called S/PDIF. :-)
http://en.wikipedia.org/wiki/S/PDIF
Even the cheapest motherboards often have these built-in.