Laymen think of language the same way they do about theory and then try to apply that to an academic context. Different meaning. A system of communication is not necessarily a language even if all languages are systems of communication. If your dog could use arbitrary linguistic tokens, generate new ones, describe things that it has not seen before, talk about the past, the future or places other than the current one, then I would be more willing to entertain the idea that your dog has a language