One way that the short story is similar to a fairy tale is in its title. "Once upon a time" is a very popular and familiar refrain in fairy tales. Another way it is similar to the fairy tale is that it opens up with an ideal world, consisting of something similar to a king, queen, and prince (the father, the mother, and the child) who love each other very much and are concerned in the protection of their kingdom (the family and their home.)
One way it is not similar to a fairy tale is in its ending, where there is little in way of a fairy tale revealed in the horrific death of the son. Another way it is different from a fairy tale is in its opening, where the author injects herself as part of the narrative. This frame story approach, where one story is told in another, is not like a fairy tale, which is very directly told with a detached narrator.
In dramatizing it for television, I would open with a flower draped garden and a panoramic shot of the family being happy. I would keep breaks to a minimum, as each act of the family's creation in the name of protection is actually one of destruction, in that it brings them closer to the climax. One of the objects which are repeated to bring symbolic attention would be the sign of "You Have Been Warned." Meant as a threat to would be intruders from the outside world, it seems like the statement applies to the family, for they receive warnings about the outside world from the servant, the mother in law, the news media, and their own fears. It seems like each time they take a step to try to protect the family, they "have been warned," of another measure that need to be taken.
It also serves as a sign of their impending tragic conclusion, as they "have been warned" of the monster that walks not in the outside world but within their own confines. The family certainly had "been warned" of the threats in the outside world. Yet, they had not been warned of their own sense of fear and paranoia, the type of emotional freight that paralyzed them from examining their own predispositions. It is the fear and this paralysis of reflection which is responsible for the child's death. The family never paused their escalating sense of freight and analyzed whether or not they were being reactive or acting in a proactive manner that sought to understand problems in a manner that represents careful and judicious thought. This lacking is the result of the boy's death. This is highlighted in the last paragraph, as each protective element mentioned helps to underscore not the desire to keep the family safe, but rather the fear and paranoia that has taken them over.
In seeking to duplicate the heroic tales from other fairy tales, the boy seeks an object that can be overcome through climbing. The wall represents this. The glass pieces that were meant to keep outsiders out, end up fatally wounding the boy and preventing anyone from rescuing him. Another symbol that is repeated and whose presence, literally and figuratively, looms large is the protective wall the family builds. Designed to keep the outside world from entering, its presence grows in height and elaborate means of protection as the family's fear grows. It becomes unimaginably high and dangerous as the family's fear reaches its zenith, contributing to the death of the son.