The author has written a number of articles on white flight. He's just couched it in different language for this publication, because the Atlantic is left-leaning and the readership likely wouldn't appreciate that term.
Also, on a factual note: every single Google search and a review of Census data and other counts of population show that LA and NYC increased in size during the time period covered by the article, which contradicts the title and summary of the article. The growth rate for both cities has shrunk because there's not much more room for either of them to physically grow, and as the 2 largest metro areas in the US, large %-based growth is extremely difficult.
It's very easy for Bumpkin, Idaho to grow by 10% over a decade if it's only starting from 50,000 people. That would be a rounding error in terms of NYC or LA population statistics.