You're mixing the ideas of communication and language. Communication is not language. Language is a type of communication. Language involves the use of symbol

You're mixing the ideas of communication and language. Communication is not language. Language is a type of communication. Language involves the use of symbols in a grammar that is sufficiently complex enough to facilitate recursive structures of arbitrary length. I think it is likely that many animals like birds, cetaceans and elephants can use language and that it is possible that some dogs and cats can too but your example of a dog understanding that the word walk correlates to going for a walk is not an example of a dog being able to grasp human language. My mom has Shelties which are a disconcertingly smart herding dog. I've witnessed one of her dogs overhearing relatively complex sentences, pausing to parse them, and then acting on the in away that indicates that they understand not just the correlation between subjects and objects but also the conditional logic in the sentence.