Does Abandon Hall count as a choose trigger?

Yes, the ability on Abandoned Hall involves "choosing" a unit, and this selection qualifies as a "choose" event for the purpose of triggering other abilities.

According to RiftJudge FAQ #10297, when you resolve the triggered ability from Abandoned Hall and select a unit to receive the +1 Might, you are actively choosing that unit. Therefore, if a card has an ability that triggers "when you choose me" (like Irelia, Fervent), it will trigger when selected by Abandoned Hall's effect.

This is because the requirement to "give a unit they control here +1 Might" forces the player to make an active, manual choice from among the available units at that battlefield, rather than the game programmatically selecting the unit.