I think this is due to a wifi driver issue.
FWIW, I just upgraded my very similar NUC5i5RYH from Windows 8.1 to Windows 10 and I have no trouble with Shutdown. I do NOT run Intel Ready Mode (have you tried disabling that temporarily?), and I did not install any drivers after the upgrade (before the upgrade I probably had slightly earlier versions of chipset/ME/graphics/wireless(17.16)/LAN & CIR - not Bluetooth since Windows seems to pick up something automatically and I rarely use it).
Update: I've since re-installed latest chipset/CIR/LAN & BIOS - shutdown still works fine. I have no idea what should be run within the ME zip, and I hesitate to install latest wireless since you thought that might be the trouble. My graphics version from Microsoft is 4256 although Control Panel-Programs still shows Intel's 4222 which I was running on Windows 8.1 before upgrade. (I haven't yet noticed "flickering" trouble after resume from sleep which had been a problem on my 1920x1200 monitor using various graphics drivers under Windows 8.1.)
Thanks. Uninstalling the WIFI driver fixed the shutdown issue. It actually was causing the computer to hang at other times as well...not just shut down. I'm still having other driver issues though.
Please reset BIOS settings; then, run Microsoft® Windows update.