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.