Kirk never had trouble annihilating single-member species such as the Salt Vampire, Vaal, Landru or the Doomsday Machine. And the only thing that stopped him from destroying the entire species of Space Amoebae was that he could only access one individual. Nothing about this appeared to be contrary to his 23rd century Starfleet general orders.
The Salt Vampire and the Space Amoeba were threats to his ship. He really didn't have much of a choice. Vaal and Landru were machines, not people and not representatives of a species.