Of course a leader must understand, at some level, what their followers are doing, but sufficient technical knowledge != is an engineer.
Take Kennedy + LBJ and the space program, for instance. Two leaders, less technical than Musk, and they still made the moonshot happen.
I think Mr. Musk could be called an engineer being technically trained in Physics and being a self taught programmer - while not technically under the engineering umbrella I've grown to accept the folks who are technically Physicists (especially applied), Mathematicians, Computer Scientists, Chemists, etc. but whom work together with engineers to develop new products (including software) as all under the same umbrella. Doesn't everyone? They all require similar systems approaches the the management and understanding of complexity.
There is a great book on this - "The Decision to Go to the Moon" by John M. Logsdon. Kennedy's great contribution wasn't really technical leadership, but political. To call for and fully support a totally Civilian Moon Landing program. To this day I am amazed by his honesty and the vision it must have taken to take such a large step and commit several percent of the Federal Budget to such a long term, risky and public program. He stood up trying to sell it and said "we will have to invent metal alloys that do not yet exist".
Beyond the political support to go do it (which is truly amazing in it's own right), it was really the technical leaders at NASA that made it happen (Mueller, Von Braun, etc.), I would credit them with truly leading the program. Sadly Kennedy really only got to kick it off...