I think there's a clear difference between an animal that's a known nuisance and any other. If a rat and an emu both wander into my yard, the rat's life is forfeit, but I'm not gonna fuck with the emu for multiple reasons.
So, the French person has pests in their home, and they and their cat are targeting those pests.
The guy with food in his hand was having that food stolen by a pest, and he exterminated that pest.
Those both really fit your criteria for pests. Gull guy did not target the bird because he saw it on the street, but because it was directly threatening his food.
Because of all the garbage