A mini-HDMI to HDMI adapter will not impact the presence of HDCP on the signal, it merely changes the connector passively. As to whether your Nikon uses HDCP or not, I'm unsure. My Canon 5D Mark iii also uses a mini-HDMI output and the first couple cables and adapters I got didn't connect very reliably, so I had signal issues until I found a cable that worked well.
You may be having a similar problem to this or it could be HDCP causing issues. I'd recommend two things you can try in order to troubleshoot this issue. First, try connecting a known HDCP signal, such as a bluray player to your capture card and see what happens. It may simply give no signal or it may give an error. If it gives an error, then you will know that your camera is simply not connecting (unless you get the same error about HDCP being present).
If this is inconclusive, you could also try connecting the camera to a TV that supports HDCP or connecting another mini-HDMI device to the capture device and see if either of those situations work.
It is possible that Nikon may have actually included HDCP in an anti-consumer move intended to prevent use of DSLRs for high end video production, but this seems like an odd choice for them as they have no product in that market segment. (HDCP would allow connecting to TVs, but prevent use in recording and most video mixers for event production.)