First of all, they are not saying there is one true metric that rules them all. They said each site will have one key metric, which makes a lot of sense. Each site will most want to measure how users engage with their domain. The example mixpanel offers is that Instagram wants to know how many users uploaded a photo. This matters way more than pageviews, etc. It tells you something about user engagement.

The bigger issue I see in your comment is that sites at different stages in their lifecycle will want to measure different things. Customer lifetime value is the most important number for a mature business but early stage startups are nowhere near getting a realistic number for customer lifetime value. If I am the founder of a startup I want detailed knowledge of how users are interacting with the product I created to address a problem domain. I can get that info immediately after I start acquiring users, well before I have an idea of whether I have a viable business and what my customer lifetime value is going to be.