What is the purpose of the short story "The Open Window" by Saki?

The purpose of "The Open Window" is to show that people can be deliberately malicious and cruel, especially to people who reveal their vulnerabilities. We know that the main character, Mr. Nuttel, has shared his nerve disorder with his hosts. In fact, his hostess, Mrs. Sappleton, says he "could only talk about his illnesses."
The fifteen-year-old Vera, Mrs. Sappleton's niece, also finds out that Mr. Nuttel barely knows her aunt. She takes advantage of this information to deliberately frighten Mr. Nuttel with a false story. Vera lies and says that her aunt's husband and two children disappeared one day while hunting. She explains that Mrs. Sappleton keeps the window (what we would call a French door) open in the deluded hopes they will walk back through it one day. Of course, they are quite alive. When they come in, Mr. Nuttel runs off, thinking he's seen ghosts.
The story implies that Mr. Nuttel is a bore about his illnesses and that Vera is getting revenge. It warns that people like Vera, despite polite manners, are not all sweetness and light. They are capable of manipulation and amusing themselves through cruelty. We all have an aggressive streak, which can come out passive-aggressively in how we treat people. The message of the story is not to assume that people have your best interests at heart.

When determining author's purpose, think about the acronym P.I.E., which stands for "persuade, inform, entertain." A story's purpose can usually be understood from these three points. The purpose behind Saki's short story "The Open Window" is to entertain. Vera, a young and mischievous girl, sets up an unassuming and sickly man, named Nuttel, for a practical joke. She tells him a story of a family tragedy only to pull off an ironic twist that frightens the man out of his wits. Not only is Vera a great storyteller, but she is also a great actress. She doesn't just tell the "facts" about the family tragedy that supposedly cost the lives of her aunt's husband and brothers, but she dramatically displays sorrow, and then believable horror, when the men return from hunting. When Nuttel runs from the home without a word to the hostess, the joke is successfully executed, and the intended entertainment is accomplished.