> What qualifies someone as an engineer?
Depends on the country. In some, it's a certification that comes with responsibilities, in others it's just a job. In any case:
1) he hasn't got anything that comes close to an engineering qualification (no, dropping off a Ph.D. after a a B.Sc. is not enough);
2) his job does not involve anything like an engineer's job, which is to "invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the limitations imposed by practicality, regulation, safety and cost." [1]
He is very good at ordering people around, but there is no evidence that he did any of this at any point (though there is a lot of evidence that he got some underlings to do the boring work for him). Again, dumping a pile of money on someone to do it is not the same thing. I can respect that he did take some risks with his investments.
Even if you have an axe to grind and are frustrated by some people not considering software engineering as "proper engineering" (which is how I read your post, though Musk certainly is not a software engineer either), writing CSS for a living is closer to engineering than what Musk is doing.
[1] e.g. https://en.wikipedia.org/wiki/Engineer