One important theme of this satirical short story is revealed in the symbolism of the characters' names. There is Framton Nuttel, Mrs. Sappleton and the niece, who is both a "very self-possessed young lady of fifteen" and a "child." Let's look at these and find the theme alluded to.
The name Framton indicates someone who is reclusive and aloof and given to worry and mental tension. This sounds exactly like the character Saki presents. The surname Nuttel (Nuttall) is a place name indicating someone who lives in and tends a nut grove. "Nut" is also slang for a foolish person or a person who is thought mentally unstable.
Sappleton appears to be a made-up surname derived from the Old English 'sæp' that has come to be slang for someone who is foolish and gullible. This perfectly describes Mrs Sappleton in regards to her manipulative niece.
We learn the niece's name is Vera, ironically meaning "faith" and "truth." She is the pivotal character, and we can deduce something about her from her descriptive tags. She has the appearance of being a mature and trustworthy young lady as she is "very self-possessed" yet the narrator calls her a "child" when she begins her tale:
"Her great tragedy happened just three years ago," said the child; "that would be since your sister's time."
The dominant theme that emerges from the satirically symbolic character names and this satirical description is that of what foolish, gullible and mentally strained people do to themselves and allow to be done to others. The mentally stressed "nut" allows himself to be manipulated and tormented, even by his sister who insisted he visit this part of the country. The foolish and gullible "sap" allows herself to be fooled and tricked by her niece and becomes an accomplice to the harm her remorseless mischief causes to innocent people (one must suppose this is a past-time of long standing with the self-possessed niece). Thus the theme is the harm done by foolish and unstable persons to themselves and to others.
In addition, the niece introduces the equally strong theme of appearances versus reality. Her name indicates this theme since she is not very faithful to the truth in what she tells Framton or her aunt. While she appears to be a self-possessed young lady, she is in reality a mischievous child, just as while the approaching figures appear to Nuttel to be ghosts, they are in reality the returning husband and brothers.
In the deepening twilight three figures were walking across the lawn towards the window, they all carried guns under their arms, and one of them was additionally burdened with a white coat hung over his shoulders. A tired brown spaniel kept close at their heels.