Is Audio Engineering Really Engineering?

I think what you have is another aspect/definition of the word engineer. It can also mean operate/manipulate/rig. It's the same kind of meaning that's applied to a train engineer, who operates/manipulates an already constructed piece of equipment (the engine). A sound engineer, engineers or designs and rigs the audio equipment (the sound engines) and manipulates the resultant sound to fit a desired need or effect. In many cases, train engineers and sound engineers are sometimes the best people to help design and construct said equipment.