I co-founded Everlane (http://www.everlane.com). I'd agree with these three priorities, although I wouldn't use those words. A customer who comes back to your site, does N things, but doesn't purchase is telling you something -- you just have to be clever enough to find out what that is.
But decoupling engagement from revenue puts you in a mindset that leads to more interesting product decisions. For example, the "love it" button on Modcloth might only be weakly correlated with revenue for the people loving it, but has secondary effects when it comes to sharing on Facebook (distribution) and filtering products by "love" for other customers (monetization for those other users).
More simply: a user who never buys a single thing but shares your site with 1,000 people who then do buy something is really valuable. A revenue-only mindset makes it hard to see that.
I'd prioritize retention over engagement, personally, or maybe the author means engagement in a way that encompasses retention.
You don't really get a sense for engagement until your product is being used on a large scale. That's the true test for engagement. That's why distribution should come first.