Out of curiosity, what is your definition of a "real" engineer.
Or to put it another way, why isn't someone who writes software worthy of the title "Engineer"?
> Do people who work in software startups generally take Physics, Chemistry, Calc 1-4, Diff Eq, Statics, Dynamics and so on while at University?
That is kind of a broad question. But I can tell you that at Berkeley, everyone in the School of Engineering takes those classes, whether you are going to be a materials engineer or a software engineer.
Edit: I'll throw this out here too:
Definition of Engineering: The application of scientific and mathematical principles to practical ends such as the design, manufacture, and operation of efficient and economical structures, machines, processes, and systems.
I would posit that someone writing software uses scientific (debugging) and mathematical (algorithms) principles to practical ends.