Is that a gerund-like construction? A noun phrase? What kind of part of speech is that? I apologize in advance if there is some thread that already deals with this issue, but since I don't really know the name, I didn't know where to look. Have a great day!
It's a verb phrase whose head is a present participle which is being treated as a noun in the context of the greater sentence. Which is very the definition of a gerund, yes. So "his being a great writer" is a gerund clause, in which "his" marks the subject. (Whether that subject is to be marked using a genitive or an accusative pronoun is actually an interesting question, but it has been addressed in great detail elsewhere on this site.)