I can't get the original NYT article as it's behind a paywall, but I don't think it's hugely necessary as you have the gist of it in your title.

Here's a video of Malcolm X responding to the story some time later, and I've typed out a quick transcript below.

Interviewer: Malcolm X, you were involved in a controversy some months ago with your leader, is that over with? Malcolm X: Well uh, I've been silent for the past ninety days, because of, uh, some statements I made concerning the President of the United States, which were distorted- Interviewer: They were distorted? Malcolm X: Yes, they- Interviewer: what did you say Malcolm? Malcolm X: Well I said the same thing that everybody said. That uh, his assassination was the result of the climate of hate, only I said, that the chickens came home to roost, which means the same thing. A climate of hate means that this is the result of something. And when I said chickens coming home to roost, I said the same thing. Interviewer: You did not say that you were glad that the President was killed? Malcolm X: No, that's what the press said. What would I look like saying I'm glad the President was killed?

So essentially what Malcolm is saying is that JFK had helped to create the 'climate of hate' that led to his death. One article I saw suggested that this would be evidenced by the Vietnam War and the coup d'etat against Ngo Dinh Diem that was orchestrated by the CIA. Kennedy had never meant for Ngo Dinh Diem to die, but the consequence of the coup was just that. Diem was killed on 2 Nov 1963, and Kennedy 20 days later, on the 22nd. I wouldn't suggest that there was any connection between the two deaths, but Malcolm X was later against the Vietnam War, and I would think he was anti-American involvement in the coup d'etat in South Vietnam.