Some manual driver installation work should do the trick:
I suspect the reason for this error is that the new driver (6444 or 6471) is DCH with 2-part ID whereas the existing driver (6287) is legacy with 4-part ID. Windows standard policy will normally disallow a newer 2-part ID driver from replacing an older 4-part ID driver.
To work around this, the existing legacy 4-part ID driver must be fully uninstalled first. Follow the steps outlined in my previous post to uninstall the existing driver, restart Windows to run the inbox "Microsoft Basic Display Adapter" (a.k.a. generic VGA) driver, then run the exe installer of the downloaded 6444 (or 6471) DCH driver to install.
Yes, I know this is a bit of a hassle, but transitioning a driver from legacy to DCH can be full of pitfalls, and the Intel Driver & Support Assistant may not be quite perfected (yet?) to properly support such a driver migration. DSA certainly cannot override Windows standard driver policy as well.
Try to upgrade your driver manually. Download the latest ver. 6444 https://downloadcenter.intel.com/download/28437/Intel-HD-Graphics-Driver-for-Windows-10-for-Intel-NU... . Unzip the downloaded archive and click on igxpin.exe to start the installation.
Based on my experience, running igxpin.exe to install 6444 or 6471 graphics driver doesn't always work. The error reported in this thread is likely the direct result of Windows disallowing a 2-part ID driver from installing over an existing 4-part ID driver. Whenever the Intel graphics driver running in the system is 4-part ID (i.e. customized), running an installer from a 2-part ID driver (e.g. 6444 or 6471 DCH) will result in this failure, which is by design to prevent customized drivers from being removed/replaced from a system.
To work around this, the existing 4-part ID graphics driver must be completely uninstalled first.
I recommend temporarily disconnecting the NUC from internet to prevent interference coming from Windows Update downloading & installing a graphics driver by itself.
Go to Control Panel -> Programs -> Programs & Features and select "Intel (R) Graphics Driver" to uninstall.
After restarting the system, confirm in Device Manager that the Display adapter has changed to "Microsoft Basic Display Adapter". If Intel Iris Plus Graphics 655 is still visible, right-click on this device and select "Uninstall device" & check the "Delete the driver software for this device" checkbox. Then restart the unit as requested.
Once the display device has changed to "Microsoft Basic Display Adapter", running the igxpin.exe installer of 6444 or 6471 graphics driver should complete successfully.
Internet connection to the PC can then be restored.