Insofar as I fit all the criteria you're listing, those traits are all things that push me to want to work on a small, independent product where I can dictate the vision for it. If I'm willing to "learn programming somewhere along the way as a necessity" to express that vision, there's no reason I won't also decide to learn how to start and run a business "along the way, as a necessity."
To put it another way: in the games industry, the "product engineers" there are called "game designers." Game designers don't generally work as freelance consultants, or put themselves on the market as employees for companies like EA or Sony to snatch up. Instead, if you have the actual vision required to come up with a decent game, you'll make it—and sell it—yourself, either as a one-man show, or by starting your own small games company.
The only game designers working for the big games companies are the ones that grew into that role from whatever they got hired to do (usually either programming or art)—and, even then, only embraced their roles once the company decided to start letting them come up with products "from scratch" that they could basically run as their own little ventures, rather than just stewarding along some existing product of the company's.
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† I say "entrepreneur", but not in the typical HN meaning of the term. Most "startup founders" I ever hear about seem to be either pure-engineering types who just think about cool tech all day, or pure-business types who think about what'll be profitable all day and follow trends. Entrepreneurialism seems to actually be much more common outside Silicon Valley in regular-old small businesses, where someone with a "product vision" like "feeding people really weird pizza" will get a loan and set up a pizza place to fulfill that vision.)
