Google's search department is in the business of identifying "good" websites, but if webmasters are creating websites that rank highly in Google, that creates a bit of a feedback loop.
"Create websites for you visitors, not for Google" isn't some kind of distraction they're throwing out. Sure, the vagueness of the statement can be frustrating, but I think that's because they honestly do not want to dictate to webmasters what makes a good, popular, relevant website. They don't truly know.
Basically, I get the sense that Google wants you to tell them what makes a good website by actually building a website that your target audience finds valuable. You're not suppose to make sense of the algorithm; the algorithm is supposed to make sense of the web. It can't do that effectively unless people ignore it and do what's right for their audience, not what what's right for Google.