I performed your test with the D34010WYK, same motherboard with i3 processor and Microsoft® Windows 10 64bit.
Results: After restarting the system, the main monitor (plugged to NUC) turned on and WIDI monitor turned off. However, as soon as I enable Intel® Wireless Display with windows key + K, the main monitor turned off and WIDI monitor on.
Microsoft® Windows 10 by default has disabled WIDI, it is necessary to enable it manually.
Yes, that's exactly what I got. I was curious to see if it reacted the same with the dummy plug attached instead of the monitor. Using the WIN + K + Enter keys isn't as clean as it working automatically, but it still gets you there.