Google is far from an engineering led company today. It is the same product management situation as at any other company. That engineering led vision for the company is what produced their early successes. Their later failures aren't because of being an engineering led company...
I think the turning point was the Google+ failure. It was perhaps the first major initiative at Google that was not engineering led, and when it failed, it seems like the shift began in earnest to restructure the company for top down initiatives, led by business instead of engineering.
Google+ indeed happened under Page's leadership, so I agree with you that this is where it fell off the rails, but I think you have the reason backwards.