YouTube music on ZENith?

Is there a way to listen to YouTube music through my ZENith?
There is no official way to do this. You could use the third-party AirPlay plugin to stream music from an iOS device to your system. That said, in my experience, the audio quality from YouTube and AirPlay is rather poor, so take that into consideration.
 
Similar to Apple relying on Airplay for sending their audio around, YouTube Music is leaning on Chromecast for this. Similar to the plugin Dan mentions above, there may be a Chromecast bridge plugin but will certainly be a 'YMMV' situation. Quality-wise, I suspect it would not be greatly different from Airplay.

You don't need to worry about Airplay or Chromecast being a negative impact on quality, as YouTube Music maxes out at 256kbps anyway which is well within Airplay/Cast bandwidth.