"The Invisible Japanese Gentlemen" is told from a first-person limited point of view. That is, there is a speaker, an "I," from whose perspective the story is being observed. It is limited because we only know what is going on in this narrator's head and are limited to what he can see and hear.
The setting is established from the first line: "There were eight Japanese gentlemen having a fish dinner at Bentley's." Bentley's is a London restaurant where all the characters in the story are dining.
There are several themes you could land on for this story, but the most prominent one is perhaps that of patience and proceeding with caution: don't get ahead of yourself, and don't count your chickens before they hatch. The narrator is listening to a young woman talking to her fiance about a book she is to have published. She is certain that this, her first novel, will be a hit due to her impeccable "powers of observation," which she prattles on about.
She believes that the money she earns off the book will surpass her advance and that it will be such a hit that her second novel, which she has already decided will take place in St. Tropez (not a cheap place to do research), will be an easy sell. In other words, she is naive, overconfident, and not a little full of herself. In contrast, the narrator is an accomplished writer and understands how taxing and unforgiving the profession is. His doubtful interjections alert us to the fact that this woman is moving far too fast.
Throughout the story, even as the narrator confesses, "I found myself hoping that [her book] would prove to be a disaster," there is still the possibility that this young woman is indeed a talented novelist whose book will sell thousands of copies. But the thematic message of the story is driven home at the end when, after her fiance mentions the eight Japanese gentlemen (who were loud and animated throughout their meal and sitting at the table next to hers), she asks, "What Japanese darling?" She hasn't seen them. Powers of observation, indeed.