In colloquial terms, think we'd find few who'd argue humans flying around in helicopters shooting elephants with high power rifles are not more evolved than said elephants.
> Consider it a big parallel hill-climbing problem with each animal being a local optimum for its environment.
There is rarely "its" environment. Because environment is shared. Especially shared with humans, who have great ability to manipulate said environment (usually for the worse). They will polute it, introduce other species which would end up dominating the food chain, completely change the physical form (built a dam and alter the course of a river), end up enslaving species in order to provide food for themselves. Would you say chickens have evolved and got to an optimal point? Or have they been evolved by humans so they can turn into dinner.
> Consider my dog: ... would you really call one of them "inferior" to the other?
I would call the organism which types on the computer, connected to an artifically created world wide network, and who is able to contemplate the fate of the universe, evolution and other concepts, a bit more evolved ;-)