A lot of this probably depends on what you mean when you say "NAS".
Since you can run Media Center on it, that already makes me think that you really mean a computer that you're using as a storage device, rather than a dedicated NAS box.
Whether this is Windows-based, Linux-based, or something else really makes a difference.
With a Windows-based machine, there are tools like VB-Audio's VBAN which can route audio to other devices over a network. I'm sure there must also be solutions for Linux.
I haven't used it, but in theory you could route the system audio from one PC to the other via VBAN and then get that to output to Media Center's WDM driver.
Of course it would be even better if Media Center could stream WDM audio to another device without the need for third-party software.
There are two problems with that right now:
1. The WDM driver no longer works on Windows 10 without disabling system security features, until JRiver update the driver.
2. Even when the WDM driver is working, I have had issues with VB-Audio's other products like Voicemeeter Banana and the WDM driver - the WDM driver played back distorted audio no matter what settings I used. So that's something else which likely requires an updated driver.