Also tried, Ubuntu 16.04 LTS - same issues with graphics - both with open source and intel drivers. What a waste of time.
Ok, at Linux you need the correct kernel and driver, but because you have the same effect at both windows installation (and the same at Linux) I would say it's a HW problem and time for RMA...
Of course something could also wrong with the RAM (or maybe the HDD/SDD)...
Have checked with two different HDD and SSD and then different RAM sticks.
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For Windows 10 try uninstalling the graphics driver and reinstall it.
Do you have the latest BIOS version installed? If not, please try updating the BIOS, you can see BIOS Update Instructions for Intel® NUC
Make sure you have all the drivers installed, chipset driver, management engine driver etc.
Downloads for Intel® NUC Kit NUC6i5SYH
As I wrote, seems to be a HW-issue at the board (because tested with different OS / RAM / HDD)...
RMA via https://customercare.intel.com/?lang=en-US (and select your country/language)
As a last action before RMA you can try to use the defaults at the BIOS/UEFI (via F9)...