Thanks for your comments Nyssa and Issybird.
I think that "The Open window" is, in part, a light satire on the Edwardian obsession with the supernatural. I think an important part of the fun is that Saki doesn't make Frampton Nuttel a particularly sympathetic character, after all, look at the weird name Saki gives him! Perhaps he's rather a bore as well as overly self-absorbed and credulous {as Issybird pointed out}. So Saki cleverly directs our attention to the "self-possessed young lady" and the story she tells thus causing the innocent remarks of Mrs Sappleton to suddenly take on a deeply sinister meaning with hilarious results. The danger, of course, is that if Saki's rhetoric doesn't work the girl becomes quite awful and Nuttel a pitiable victim. But I think he succeeds.
"The Boar Pig" is a good example of Saki pitting tough, smart, imaginative children against dull, stupid, unsympathetic adults. Mrs Phiidore Stossen is a pretentious social climber and gate-crasher. Her daughter clearly goes along with the whole attempt to crash the garden party. {the comment about gooseberry bushes reminds me of the world of "The Lumber Room"--perhaps Saki is using the same setting}. Now, is Matilda Cuvering really a mean brat? One can certainly argue that. Matilda is rather mean to Claude. Interestingly, she is obviously quite clever, but certainly
not regarded as a "good" child; that role is filled by her young cousin, Claude--who follows the rules. As in "The Lumber Room" Matilda uses the arbitrary rules imposed upon her by her aunt against the gate crashers. Thus, she makes fools of them and makes some money as well. Was justice done? Well, maybe.
I think that Saki shows children of this type because they need to be tough, smart and a bit ruthless in breaking rules to retain their sense of identity in a society which doesn't approve of independence of mind and spirit {at least in children}. I think the same pattern is in "The Lumber Room", "The Story Teller" and even, to some extent, in “The Schartz-Metterklume Method”.