The main characters of the story include Rose, a young girl, her father, and Flo, her step mother. Rose and her half brother live with their parents in a poor Ontario town, earning a living running a furniture repair shop.
The time in which the story is set (the Depression) is a significant backdrop for the story. The dilapidated nature of the town and the run down quality of the shop are symbolic of the worn-out emotional state of the characters. The details of the shop, with its pieced-together floor of scrap linoleum, or the falling-down houses patched with tin and cardboard, become a backdrop for the central conflict of the story, which has less to do with Rose's punishment (the "royal beating" of the title) that with the alienation of all the characters.
In terms of narrative style, Munro uses a third-person omniscient narrator. The story is told primarily from Rose's point of view, but the narrator has access to the feelings of all the characters. It is through this flat omniscient narrative tone that Munro heightens the feeling of inevitability one has about the events of the story.
It's clear from that all the characters are playing a "part." While Rose's beating at the hands of her father is very real, there is also, on the part of all involved, a sense that they are engaged in a kind of role-play. The father is slow to warm to his role as the dispenser of discipline; Flo's outrage over Rose's perceived insolence is something she nurtures on purpose; even Rose's behavior is a kind of calculation. The whole process of Rose's beating, and Flo's attempt to make things up by making her a special meal, has the elements of ritual. In that sense, the real conflict of the story lies in the ways circumstances have caused these characters to cling to emotionally dysfunctional lives and embrace violence.