Hold on here a second... Found something that worked for me. Right here, from this site; Windows 10 HDMI Connection Intel Graphics Issue Disable and enable the driver, configure project once again. Odd, but I'm happy with this, until HDMI stops working again ;)

Hi, I am currently fighting with ASUS UX510UX and HDMI issues. Before this, I had UX305, which I gave up believing that its HDMI port had broken suddenly down. I was mistaken. With UX510UX I soon encoutered the same situation, HDMI ceased to function. This happened with the 1607 update and I rolled it back and this restored HDMI functionality. All was fine fore few weeks and then Win10 updated driver files (you cannot prevent this, unfortunately) and I lost the functionality again. I was in touch with tech support and they provided me with a installer that overwrote all relevant files and HDMI was restored once again... until today when some kind of a driver update once again took place (you hear that "device connected" sound and screen flickers, then you know that you just had unwated driver update). This time the provided package could not restore HDMI functionality and I am currently trying out reinstalling. Win10 built-in "Reset" is no good, even with "remove all files" option. Nothing changed and all...