Thanks Jason for your answer.
However, I have tried your workaround when I was running (K)Ubuntu but it didn't work for me.
It seems that, except for you, only OpenElec works well for HDMI sound according to what I have seen here and on other web sites. But, OpenElec is too limited for what we can do with this NUC.
Strange, because that's the solution that works for me in Linux Mint, which is Ubuntu-based. I'll have to leave it to one of the Linux experts to explain it.
I had the same problem with Lubuntu 14.04 and the above solution did not work for me either. In the end I solved it by installing pavucontrol (PulseAudio Volume Control) which gave me the option to select the HDMI output.
When installed I found it in the Lubuntu menu>Sound & Video section and launched it. Under the 'Configuration' tab I chose Digital Stereo (HDMI) Output. I believe you can also launch it by right clicking the volume icon in the task bar and choosing 'Volume control settings'.
I cannot believe the HDMI option is not switched on by default or made more easily accessible!