I wasn't around for the voting and I had never heard of Saki before but now I'm very glad to have found the recommendation here! I just read a few stories today but will read more.
For the time at which he wrote these stories the social commentary is quite sarcastic and satirical. The stories are quite absurd and too short for much character development so I see them more as vignettes about inter-class and parent-child relationships and some of the rediculous rules they were and are expected to live by.
He also seems to have an overall moral of the story which is that you should not take things at face value. You should not believe everything you are told or perhaps anything you are told.
In The Boar Pig I mostly see the silly social rules, the need to be at the party even if not invited, an attempt to sneak in, assuming it is true that the boar is dangerous. In a twist it seems she really does give the money to charity.
In The Open Window, it is rediculous to try and cure a nervous condition by visiting strangers by way of letters of introduction. The girl takes advantage of his overdivulging of information and believe anything nature to make him see ghosts. He is so eager to apply the appropriate amount of flattery and talk about his illness that he opens himself up to the joke.