The climax in a piece of literature is the moment of highest emotional intensity and the point at which the plot begins to turn toward its resolution, so in the case of "A Man Who Had No Eyes," the climax is when Mr. Parsons says, "Not quite."
In this story, Mr. Parsons encounters a blind man when he emerges from his hotel. The blind man, Markwardt, is begging for money and begins to share the cause of his blindness with Mr. Parsons. Markwardt recalls a terrible explosion at a place called Westbury; one hundred and eight people were killed, and over two hundred were injured in a chemical explosion there. Most interestingly, he shares that he could have escaped with his eyesight if he had not been pulled down from behind by a large man who "trample[d] him into the dirt." The man escaped, but Markwardt was left inside with "all that poison pouring down" around him, which destroyed his eyesight. He concludes this tale with, "That's the story, guv'nor."
Interestingly, Mr. Parsons provides a quizzical response, which is the climax of the story: "Not quite."
This comment shifts the entire mood of the story. The reader is proceeding with sympathy for this tragically injured man who was beaten down and thus robbed of his eyesight; but suddenly, it is clear that Mr. Parsons knows the man.
To respond "not quite" means that Mr. Parsons was present at the explosion and has listened to this tale with more than passing interest. He then reveals that Markwardt was not the victim in the explosion; instead, he had pulled down Mr. Parsons in his own quest of self-preservation.