You begin with the assumption (based on nothing other than a general feeling of human specialness) that "For all we know, dogs responses to human emotions, gestures, and nonverbal cues are a completely autonomic behavior". Considering that we discover all kinds of animals are smarter than we thought with each passing experiment, the burden of proof should lie with you. The limitations appear to be our experiments.
We do not start with this assumption when dealing with human beings. The safe assumption is that animals have their own desires, goals, ambitions, and purposes for existence. Since we have significant trouble understanding them or communicating with them (even though we know that within their own species they communicate perfectly well with each other), we might start from a less biased viewpoint.
As for jellyfish, I don't know. But I do know that we've approached it from the wrong angle. Asking how many words a jellyfish can respond to and then determining whether or not it is intelligent is a surefire way to create a lousy experiment.
BTW, Europeans used to do the same sorts of experiments with people from other countries and civilizations. They knew that white Anglo Saxons were the best and brightest so they looked for evidence to prove it. Africans clearly hadn't invented guns or the printing press so they determined that they had a lower level of intelligence. It's just as ridiculous a methodology when you're talking about studying animals.