Esther 3:10, Question 2. Why does the verse repeat Haman’s genealogy here?

The Ginzei HaMelech writes that this verse mentions Haman’s genealogy to indicate that Achashverosh knew to whom exactly he was giving full reign. He knew Haman’s entire geneology, and all of the Jew-hatred in his DNA. He nevertheless gave him the ring, and all of the power that came with it.