In analyzing any story or part of a story, it is necessary to begin with the realization that the people are not real but are creations of an author. They are created to serve the author's needs and purposes. Saki made Framton Nuttel the kind of character he is because the author needed just such a character for the role of victim of that particular practical joke.
Framton is described in the e-notes summary as "an eccentric hypochondriac." He is an exceptionally nervous man. He has been to several doctors about his nervousness, and they have recommended a "rest cure" in the peaceful English countryside. This explains why he is calling on the Sappletons. Since he is going to a part of the country with which his sister is somewhat acquainted, she gives him the following advice.
"I know how it will be," his sister had said when he was preparing to migrate to this rural retreat; "you will bury yourself down there and not speak to a living soul, and your nerves will be worse than ever from moping. I shall just give you letters of introduction to all the people I know there. Some of them, as far as I can remember, were quite nice."
Framton's sister is a very minor character who doesn't even appear in the story. She was created by Saki for the purpose of giving Framton the letters of introduction which led to his visiting the Sappleton home and running into Vera.
The second reason Saki had for making Framton a nervous wreck is that it would take such a character to respond to the appearance of the three returning hunters as he did. A man in normal psychological condition might be frightened, but he would not behave in the manner Saki describes.
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.
So Framton is what he is because his creator made him the way he is. The same applies to Vera and to Mrs. Sappleton. The aunt is rattlebrained, and Vera knows exactly what she is going to be talking about when she makes her appearance. Vera is bored and wants to create a little excitement. A girl like her in her times would be confined to the house and would undoubtedly spend a lot of time reading escapist-type fiction. This is where she gets her wild ideas.
The characters never really existed. The events never really happened. The story is a creation, a work of art. It can be read for enjoyment. But if you want to analyze it, or any part of it, such as the character of Framton Nuttel, you must view him as the creation of a human mind. Saki is telling a story, and his creation Vera is telling a story within a story. "The Open Window" is a classic because it was a good idea to start with and is so well crafted.