NYC is bigger than Manhattan. The parts of Brooklyn and Queens that aren't filled with rich people (i.e. most of it), as well as the Bronx and Staten Island, are not nearly as expensive as what you might be used to.
Not to mention statistical sampling of rents is always going to skew lower than market because of rent stabilization and rent control - it measures how much people are paying, not how much they would be if they were on the market today.
NYC is 8.5 million people, only ~1 million of whom live in Manhattan.
I haven't looked at the data itself, but if their measure of NYC is the NYC Metro (rather than the city proper), rents will go down too, since now we're including most of North Jersey and a lot of Long Island.
The missing piece is that (relatively) cheap real estate is not advertised, you need to get it from a friend who's leaving SF. It can be frustrating sometimes that good apartments are allocated by seniority (how long you've lived here & who you know) rather then by the free market.