Why do you think that the author gave us the information regarding Mr. Nuttel's ailments?
We are told at the beginning of the story that Framton Nuttel is undergoing a "nerve cure" by spending time in the country. The only other details of his ailments are those he gives to Mrs. Sappleton.
"The doctors agree in ordering me complete rest, an absence of mental excitement, and avoidance of anything in the nature of violent physical exercise," announced Framton, who laboured under the tolerably widespread delusion that total strangers and chance acquaintances are hungry for the least detail of one's ailments and infirmities, their cause and cure."
The author gives us this information about Nuttel's ailments because the ending will be all the more hilarious when we see that he is getting just the opposite of what the doctors wanted him to find in the country. He is not getting "complete rest" because he has to run for his life. He is not getting "an absence of mental excitement" because the precocious Vera's story has resulted in more excitement than he has probably ever experienced before. He is not avoiding "anything in the nature of violent physical exercise" because he goes running out of the house and up the road thinking the ghosts are after him.
Framton grabbed wildly at his stick and hat; the hall door, the gravel drive, and the front gate were dimly noted stages in his headlong retreat. A cyclist coming along the road had to run into the hedge to avoid imminent collision.
The author has no sympathy for Nuttel. Neither does young Vera. They see him as a neurotic and a hypochondriac who has nothing really the matter with him. Mrs. Sappleton simply sees him as a bore. Perhaps his experience at this peaceful English country home will do him more good than "complete rest, an absence of mental excitement, and avoidance of anything in the nature of violent physical exercise." At any rate, he will be unlikely to intrude on any more strangers with his letters of introduction.