How does SEO for Google Shopping / Merchant Center, work?
What you are talking about of course is Google's Merchant Center. It is impacted by whether you have a keyword-heavy XML feed (properly configured in Merchant Center), plus REVIEWS. Merchant center is heavily influenced by reviews. So just as links impact SEO, for Merchant Center you need links, a.k.a. reviews.
I agree for product searches Merchant Center / Shopping may be as important or even more important than the main Google search page.