The ROCK guide says this:
We have had a few reports that NUC10ixFNxN models (the one’s that end with an “N”) do not have Intel HD Audio Support and thus won’t be able to expose their HDMI or local outputs to RoonOS.
Your NUC model doesn’t match but it describes your symptoms exactly. Even without HDMI, at least the headphone output should be available. You might have just been unlucky and stumbled upon another model that doesn’t have Intel Audio Support.
Check out the other thread and see if there are other clues you could follow up on. Does your NUC have a headphone jack in front?