I got an automatic Windows Update yesterday on my Intel NUC D54250WYK. After the reboot, I discovered that I had no "HDMI audio device" anymore, but only the "Headphone audio device". Re-installing "Realtek Audio Drivers" didn't solve the problem. The trick is to uninstall and re-install both the Audio Drivers AND the Graphics Drivers!
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Get both Audio and Graphic Drivers from the Intel Download site (I.e.: "Audio: Realtek ALC Audio Driver for Intel® NUC" and "Graphics: Intel® HD Graphics Driver for Intel® NUC").