Sadly a relevant thread was closed for being “5 month old” 
really…
So here goes. This is one potential solution. In my case uninstalling and re-installing the Realtek sound driver fixed it. Now WoW automatically switches audio output (Speakers/Headset) like every other software does.
Don’t buy the nonsense that WoW is not designed for such functionality, no software is created this way. It’s nonsense and BS from people who simply don’t have the dignity to say they do not know what the problem is and can’t offer a solution.