Seriously, though, I'm quite undecided whether he is a Black Númenorean or an Orc chieftain. He being a Nazgûl is out of the question - at least for me - since it doesn't seem to make sense for the Witch-King to have another second-in-command other than Khamûl.
Oh, and as
Hookbill said, the Orcs serve Sauron in fear, plus they barely show any influence or aura of authority over their fellow bad guys.
That leaves me with the second option - that Gothmog is a Black Númenorean who rose to the heights of Sauron's army the way Grima probably did in Rohan.
Maybe Mouth and Gothmog were close buddies in Númenor?