I have spend literarily days figuring out this problem. When I fresh install Windows 10 on my Shuttle DS81 I get audio over HDMI when connecting my LG TV to it, then something changes on my system and I got no audio over HDMI.
Turns out that disabling Hyper-V fixes the problem.
I think installing Microsoft Visual Studio 2015 enabled Hyper-V but I’m not sure.
On this device audio over HDMI is more important then Hyper-V, but I still like Microsoft to fix this problem. This problem exists since a technical preview somewhere begin 2015 and even exist in the current release build of Windows 10.
The weird thing is, that every things seems to work fine, the green bars are showing, just no sound over HDMI: