Well, since Tolkien never gave us a definitive answer (absent any undiscovered manuscripts), I would say that Gothmog could be any of the three. It's down to the reader.
On that basis, my vote is for
Nazgul since, in an old
War of the Ring game that I have, he is depicted as one. And so, I have considered him to be a Nazgul for some 25 years and I am not about to change my mind now.
But even applying logic to the situation, my answer holds. I would expect the second-in-command at Minas Morgul and in the assault on Gondor to be of similar power to the commander (ie the Witch-King). Khamul, as the Lieutenant of Dol Goldur, was almost certainly directing the assaults on Lorien, the second of which occured on the same day as the Battle of the Pelennor. I would therefore conclude that the Witch-King's second-in-command was one of the other Nazgul.