He wasn't trying to kill the Joker, he was trying to prevent him from leaving. It was the Jokers own actions that caused him to plummet to his death.
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Ahem...
https://youtu.be/gaB-MWX00xo?t=47s
I guess you could argue they were the faster runners known to man and were able to all escape rather than being blown up or horrifically burnt to death...
I was talking about the Joker death specifically. He also shot at the Joker with the Bat Wing. So, yes Batman 89 was not against killing.