How does the paytan know? And didn’t Mordechai receive the estate?
You may have heard the attempted “resolutions by Rambam” of a Goy’s children being “Kinyan Kaspo”, etc. etc.
An elegant translation in Rabbi Hirsch’s Siddur (p. 688) negates the question.
כְּרוֹת קוֹמַת בְּרוֹשׁ בִּקֵּשׁ
אֲגָגִי בֶּן הַמְּדָתָא
וְנִהְיָתָה לוֹ לְפַח וּלְמוֹקֵשׁ
וְגַאֲוָתוֹ נִשְׁבָּתָה
רֹאשׁ יְמִינִי נִשֵּׂאתָ
וְאוֹיֵב שְׁמוֹ מָחִיתָ
רֹב בָּנָיו וְקִנְיָנָיו עַל הָעֵץ תָּלִיתָ
The Aggagite, son of Hamedatha, sought to cut down the lofty pine. But it becam his own snare and his arrogance was broken. The head of the Binyaminite You did raise, but the name of the foe You blotted out, of his sons and of the abundance of his wealth; and him You hanged upon the gallows.
I’m only telling you, of course. No need to change the Purim Torah!