It's pretty common for there to be secondary commercial and business districts in a city.
NYC has these already, too. Long Island City and Downtown Brooklyn, as well as outside of NYC proper but clearly in the core urban area, downtown Jersey City. Even the Midtown vs. Financial District distinction (Midtown having originally been the satellite but overtook the Financial District as the main commercial center) matches this (not all of Manhattan is the CBD).
The difference is that Long Island City, Williamsburg, and Dpwntown Brooklyn are directly adjacent to the existing CBD of Manhattan below 60th St, and are more Residential in nature.
Flushing and Jamacia are further out in Queens; it’s take someone at least 30 minutes to get between midtown and Flushing or Jamacia
Williamsburg is decisively not a business district and not worth having as part of the discussion. Nobody is suggesting otherwise.
I agree LIC and Downtown Brooklyn have gained some residential character in recent years, but they are decidedly commercial historically, much more so than any part of Flushing or Jamaica. Jamaica in particularly still has barely any commercial development, just a lot of hotels (because of proximity to JFK and transportation links) and some new residential highrises. Flushing is somewhat different as it does have
some commercial development recently, although even then the new highrises are all residential.
And it's honestly a pure mistake (the kind made by people who live outside NYC trying to analyze it) to refer to the CBD as "Manhattan below 60th St". A majority of the land area of that region is definitely non-CBD.