However, I put this point to you — was it a good thing that Haman was killed even though it was a non-Jew who did it?
Well, maybe a Jew did it. I thinks it’s not just possible but likely. At any rate, it was definitely done from a Jew’s initiative. If someone dies as a result of your actions, doesn’t it count as if you killed him?
Or, let’s put this hypothetical out to you. Amalek is engaged in a bloody war with Moab. Do we go to war with the Moabites to stop them from killing the Amalekites so we can do it ourselves, or do we let the Moabites try anyway and say that’s it’s not worth Jewish blood to save the Amalekites if others are willing to do the killing?
Or are we allowed to join ranks with them to kill the Amaleikim? (That seems to me the best solution. I guess that presupposes that what they are doing does count in fulfillment of Hashem’s will.)