From a 2025 report, yes, food deserts exist in New York City, particularly affecting low-income communities of color in the outer boroughs and upper Manhattan. An estimated 750,000 residents live in areas with limited supermarket access, while roughly 3 million live where fresh produce is scarce.
Again this 750k figure, like in that NY Times opinion piece from 2009. It's as if that unsourced figure gets passed down from author to author through time. You'd think the number would change either up or down in 16 years.
That CUNY pdf seems to be an undergrad assignment. It does not define terms. It also mentions that many New Yorkers only have bodegas nearby. First, even that is exaggerated, as I have shown above.
But, more fundamentally, in dense urban neighborhoods, there is limited space for full-service grocery stores. There is no reason why corner bodegas cannot sell fresh fruits or vegetables, if they sell in sufficient quantities to make it worthwhile.
There are also produce carts operating in NYC. You don't need a store with 10s of thousands of square feet of floor space to not have a food desert.
The other link has already been posted by Jimmy Higgins, and we already talked about how bonkers that site is.