Other possible interpretations could include that the story was funny, so it "killed" the reader with laughter; or, that the story brought to mind painful thoughts, which "killed" in an emotional sense. I'd go along with that latter, considering the personality of the main character of Catcher in the Rye.
I think the idea you are looking for is the first one -- the making of a strong impression; but all could be explored. Note, also, that is is the short story in the book, and not the book itself (same title), which provoked this reaction.
Hope this provides a starting point.