UPDATE: I restored the Windows 7 image, uninstalled the Intel HD Graphics Driver for Intel NUC using remote desktop. Now Windows Update started screaming for attention. It had an "recommended" update in the category important updates: "Intel Corporation Graphics Adapter WDDM1.1, Graphics Adapter WDDM1.2, Graphics Adapter WDDM1.3 software update released in January, 2014" This appears to be version 10.18.10.3412 and it works, provided I power on my monitor after Windows start-up. When I shut down Windows or enter Sleep Mode it leaves the monitor in a state I never saw on other systems: the screen becomes blue and it never goes in standby. If I power on the NUC again I have to power-cycle the monitor to get normal display again. Also when Windows dims the display after 5 minutes idle I have to power cycle the monitor, so this still not really workable.
I search the Intel Communities outside the NUC section and got a shock: there are HEAPS of problems with HD 4000 graphics and HDMI. There is even a "Official Black-screen thread " initiated by an Intel engineer that after almost a year still has not resulted in a solution.