Modernism
Modernist texts generally include literature written between 1899 and 1945, and often involve some sort of experimentation with traditional narrative forms. "Kew Gardens" does not adhere to any traditional genre category like "mystery" or "coming-of-age." As we've noted before, there isn't really a clear plot line. Think about how you would describe the story to a friend. It'd probably go something like this: Well, it's about different people who wander through a public garden in London in the summer—oh and also about a snail and some flowers.
Clearly, this isn't a traditional story. "Kew Gardens" is experimental in nature and is best classified with the category of modernist literature.
That said, we might note that it contains certain elements of other genres. For instance, the descriptions of the snail journeying through the flowerbed recall a classic adventure story. After all, the snail is clearly preoccupied with the risks and dangers involved in climbing beneath the tremendous brown leaf—quite an adventure for a snail.
The episodes with the married couple and with the senile man and William (possibly his son) also suggest the presence of family dramas, though these dramas are only hinted at and are not the main focus of the story.
Finally, the story also contains elements of the realist genre: "Kew Gardens" is, fundamentally, a careful description of a scene from everyday life in twentieth-century London.