Ah, I got it.
First, I did all other quests (the non-repeatable ones). Don't know if that has anything to do with it tho.
Second I took it much slower. When the allied treant started bashing in the gates I did some skirmishing with archers. Then I got one of my own treants to the wall (mind the maneater-plant) and took the walls. The allied treant was still bashing in that goddamn gate.
The cutscene in which the elf is slain started as soon as my troops were inside the enemy keep.
I clicked all the dialogues as soon as they popped up (I ignored them before).
Then I started killing orcs. It helped that I placed my archers on the walls before. After a while I got another cutscene and the quest was done.