To me "Product-minded" engineers defined here are mostly engineers who has the willingness to go "above and beyond".
Some may have this willingness because of their intrinsic nature. Some may have had this willingness but it slowly eroded because of many external factors (i.e. not getting recognized or compensated for their "above and beyond" work). Some simply have other priorities in their life (which I understand 100%, I suspect I'll be in the same boat if I had kids).
I've always seen myself as a "product-minded engineer". However, recently I'm struggling with keeping that mindset. Part of it is because of external factors and part of it is because I've also started to prioritize my personal life more. I do recognize that this is not black and white but rather a spectrum but it is so much harder to be fully engaged to a product when you are not giving it your 110%. :P
That being said I also believe it's also up to the company to foster and reward this kind of engineers, instead of just asking engineers to be a "product engineers"