I didn't know of his background, so I googled. He learnt to code while he was working a job and his first startup came later? Anyway, he doesn't seem to have done much of interest before his first startup.
The question rephrased: Show me a guy who has gone from being a success in management/finance to having a startup idea and then writing code for it (I think this is a fair equivalent of coder with no business experience founding a company and then continuing to run it when it becomes very profitable)
He worked in marketing and had ideas, so he learned to code to build them. Then the idea for Instagram came along, he built it, marketed it and sold it.
"Management/finance" doesn't mean anything, other than excluding Systrom as a specific example which disproves your theory.
You're asking to see someone who was successful in a non-technical role who had an idea for a startup and learnt to code to build it. Let me surprise you: very few people learn to code just to learn to code. Most people learn to code to scratch an itch. How many news stories have we seen in the last few years about people who learned to code simple addictive games for iPhone?
In that sense, I'd argue that almost everyone learns to code because they have an idea they want to see happen. A lot of them go on to become full time software engineers. A lot of them don't.