Millions of people voted for Trump in 2016 because they bought into his carefully-crafted image of a brilliant, self-made businessman who can drain the swamp and get things done in Washington. The NYT article was consequently intended to strike at the very heart of his appeal and his self-image.
Will it work? No, because it’s too late; everyone has already taken a position on the man based on his behavior in office. It might have made a difference in 2016, but not now; they’re just preaching to the choir.
The NYT is essentially daring Trump to sue them. You can be sure the article was reviewed very carefully by their legal team. I’m guessing he will do some huffing and blowing, but he won’t take any action, because it cuts the legs out from the argument that he should be temporarily immune from defending lawsuits because he is just too busy with his job to be bothered with such flotsam and jetsam.
Besides, truth is a complete defense.