Why do you assume mine maps to nothing? Are you really arguing that the importance of cities is based off a single economic number or simply the number of people living there? I would say it's a combination of politics, cultural relevance, and economics mainly. Going down 1-4 in no order:
New York - huge center of mixed cultures, huge both population and economic output (larger than Chicago), and a big center of the fashion industry, art, etc.
DC - Capital with lots of political relevance, still good sized and has lots of other aspects that make up a city like good public transit
SF - The tech center of a world being increasingly run by tech, for better or worse
LA - Huge global entertainment hub, huge cultural mixing pot, huge GDP and population
I find this strong backlash interesting as I have no dog in this fight - I'm from a no-name suburb to a medium city in the south and am simply a lover of cities comparing what I have encountered.