Robert Pattinson has supposedly called the movie a "slapstick western," but I have a hunch he may have intended something closer to a "western farce." These terms tend to get mixed up because they often coexist. It's common for a farce to contain some slapstick elements as a way of reinforcing the chaotic and unpredictable nature of the genre (or the spirit of the story being told), but Damsel isn't much of a slapstick anything. It's not a Three Stooges western. It is quite silly, clever and violent at times, but at its heart it is a tragedy -- one that is both funny and sad, sometimes within the same scene. And I think that's a big reason why it makes for a very successful farce.
Anderson has created his own Roald Dahl-type fable this time. Or, to be more precise, his own The Little Prince. While the Antoine de Saint-Exupéry's classic is about a pilot who crash lands in the desert and meets a little boy from another planet, Isle of Dogs is about a boy who crash lands on an island and meets five dogs who agree to help him find his beloved Spots. In case the hat tip wasn't implicit, the dogs call the mysterious fallen boy, the "Little Pilot."