I am not from Intel and I do not have that model NUC, but my guess is that there was an orange sheet of paper included with your NUC that mentioned having to go to downloadcenter.intel.com (the select Kits-NUC-model) for device drivers for hardware such as network. Whoever installed your Windows 8.1 probably neglected to perform that step (using some PC other than the NUC being installed).
It is possible to get network connection using the embedded LAN port (RJ45) or using the wireless card included in your NUC.
I recommend you to use the wire connection for the first time. The NUC will use the generic drivers from Microsoft® Windows. As “dougho” mentioned, it is necessary to install the NUC drivers.
Please start with the chipset (INF) driver version 10.1.1.8, continue with the ME (Management Engine interface driver) version 18.104.22.1688; then with the graphics driver version 22.214.171.124.4222 and finally continue with the rest of the drivers available.
Drivers for Intel® NUC Kit 5i7RYH
Graphics driver for Intel® Iris™ Graphics 6100
If my twopence is worth anything, I had the same problem yesterday after changing operating systems.
I downloaded and installed all the drivers in the NUC5i7RYH driver pack (dated 1 July) but found the LAN/Ethernet wasn't being recognised.
I went back to Intel Driver Site (using wireless) and found a later driver (dated 17 July) and installed it, and now the LAN works fine.
My work for you Joergen.