According to the Ben Ish Chai, the verse emphasizes that Haman prepared the gallows on which he dies because if the wood of the gallows was made from the beams of the Beis HaMikdash, and the Halacha as brought down by the Rambam (Mishneh Torah, Hilchos Shegagos 9:1) would not allow Mordechai to make use of it. However, since the wood of this beam has already been used by Haman, this removed its sanctity, making it usable to kill him.
According to the Ora V’Simcha the gematria of ha’eitz (“the tree”) (5+70+90=165) is the same as Haman (5+40+50=95) + 70. Seventy are the number of days Haman was in power. According to the Chida, seventy is also the number of verses between Haman’s rise to power (Esther 3:1) until his downfall (Esther 7:10). Finally, seventy is also the gematria of yayin (“wine”) (10+10+50=70). The very wine with which Haman intended to seduce the Jews of Persia to sap them of their spiritual power is what led to his undoing. This may be yet another reason for the Talmudic custom (Megillah 7b) to drink an unusually large amount of wine on Purim.
R’ Yechezkiel Levenstein writes that many people recognize that their suffering comes from their own sins, but they do not realize that the sin, itself, creates the punishment.
The Vilna Gaon writes that Achashverosh uses the word “yikaro” (“his glory”) because if Achashverosh were to have said “gedula” (“greatness”) as in Esther 6:3, Haman would have known that he was not referring to him because he was already made great (Esther 3:1).
According to the Midrash (Esther Rabba 9:2), Zeresh was advising Haman to convince the king that it was imperative that he kill Mordechai. He was supposed to explain to Achashverosh that Mordechai’s very existence threatened Persian civilization, even to the point that just his praying had the power to negate the power of their Persian gods.
For another explanation for Haman’s not needing to ask the king, but rather tell him, we should recall that the Yalkut Shimoni (1053, commenting on Esther 3:1) writes that Achashverosh had built a throne for Haman that was even higher than his own, and that the Talmud (Megillah 51a, commenting on Esther 4:1) says that Mordechai’s cry after learning of the decree against the Jews was that Haman became more powerful than Achashverosh. Based on these, the Avnei Nezer writes that Haman was to tell the king instead of asking him because he had taken charge. Perhaps, as in history or literature, the king gave his adviser greater power than he realized in order to have less responsibility, himself.