>I laughed to think that HUMAN'S analysis of whether a dolphin is intelligent is whether WE can understand their language.
>Using that logic, it seems my dog is more intelligent than me: He can understand some of my language as well as his own, whereas I can only understand my own.
That's a false equivalence, as well as untrue.
It takes intentional effort on our part for a dog to learn even a small subset of our vocabulary. When dogs learn our language, they only learn the few words that we make an effort to teach them, and these typically correspond directly to an action we demand of them in exchange for a reward. Dogs cannot pass this knowledge amongst themselves, each dog has to be taught by a human individually.
Dogs have made no specific effort to teach me, at least none that they managed to make recognizable to me, yet I can tell when they are excited, hurt, angry, &c, but mostly because a subset of body language and vocal attitude are instinctive or socially universal to most mammals (shouting and sharp poses convey aggression, for example).
I believe I understand more dog body language than dogs understand human body language. There is no human equivalent of a wagging tail, yet I understand that. There is no dog equivalent of a pointing finger, and they do not understand it: dogs will look at your finger instead of where you point.