I am not from Intel, but their Product Features says Up to 7.1 surround audio via mini HDMI and mini DisplayPort. In my experience with other NUC, if you are not getting audio out the mini DisplayPort, you simply need to download/install Intel's graphics driver bundle (which contains Intel Display Audio) instead of using some default Microsoft audio driver.
Does the NUC5i7RYH provide audio out through the mini DisplayPort or only through the mini HDMI port?
Yes Mini-DisplayPort should provide audio. HDMI carries audio too. Depending on your needs, you can also use the available audio out plug on the front of the NUC.