Update: I seem to have fixed the problem, although I'm not entirely sure how or why...
I tried re-running the driver installer, and while it was doing its thing I tried establishing a connection to my wireless LAN. At that point - and I don't know whether this is coincidental or not - the installer started to install the LAN drivers.
I checked device manager to be sure, and that is now displaying the LAN device correctly.
I had the same problem with the new nuc and also a new system based on the 270 chipset.... the intel lan driver would install, the device would show as there in device manager, but not in the ethernet connections.
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Everything seems to be working fine now, but, just FYI, the NUC already had the latest BIOS installed.