I think you're indeed arguing a sensible definition of Artificial Intelligence, but it's not what most people (especially laymen) mean by the phrase. I think most actually equivocate AI with Artificial Sapience: some cognitive architecture that can—in theory, with the right training—do all the things humans do (socialize, write persuasive essays, create art, etc.) at least as well as the average human.

Though in all honesty, I think a lot of people just want to see a machine with emotional "instincts" and an understanding of tribal status-hierarchy dynamics such that you can empathize with it. A lot of people would consider a machine that accurately simulated a rather dumb chimpanzee to be "smart enough" to qualify as AI, even if it couldn't do any useful human intellectual labor.