He will not benefit from selecting a separate audio device, because HDMI is his only digital audio output on the NUC.
The NUC does not allow to use Thunderbolt as an audio-only device, so it's not available as Kodi audio device.
TB doesn't have to be the audio device. TB3 should be quite capable of displaying 4k video (I know, no Linux HDR right now), and use HDMI for audio with a blank screen at a low resolution.
The funny thing is, in display options my only options are DP1 or default (The video is actually connected to HDMI - and works). And for audio devices it only works when the DP device is selected, not when any of the HDMI devices are selected (again, I am actually getting sound from the HDMI port). BIOS is configured for HDMI primary, TB secondary. This was also observed on this thread.
I gather that the naming is an artifact of the internal LSPCON architecture. I don't care what the devices are called. But it seems quite funny to only have one display device option regardless of what's going on with the audio devices. This may be more of a Linux on this device issue than a Kodi or LE issue.
Thanks all.