"The Snows of Kilimanjaro" is one of Ernest Hemingway's most masterfully written short stories, and it has plenty of linguistic style and literary devices embedded in the text to keep even the closest of readers occupied for a long time. Hemingway's doing a lot in this story. For our purposes, though, I think it would be best to focus on two things in particular: economy of language and symbolism.
Economy of language: this trait is a classic characteristic of Hemingway's style. His writing is most commonly known for simplicity and lack of needless stylistic flourishes. Indeed, Hemingway's prose could be reasonably compared to a strong cup of black coffee, as both are robust, plain, and simple. Understatements are a particularly key trait in this story. Often, Hemingway writes about important things in an indirect fashion; he never directly says what's happening, but the reader can guess obliquely by paying attention. In "Kilimanjaro," Hemingway doesn't immediately tell us his protagonist is dying. Rather, we're allowed to figure this out for ourselves based on the characters' indirect, clipped dialogue and a few hints Hemingway throws our way. As a result, the story's deeper meaning unfurls indirectly, so we appreciate it much more once we finally understand it.
Symbolism: all of "Kilimanjaro" can be summed up in Hemingway's brief description of a frozen leopard near the summit of Mt. Kilimanjaro at the beginning of the story. The leopard can be seen as a symbol for seeking and struggling to reach a higher purpose or meaning, but ultimately falling short in the process. This same concept is what much of the rest of the story is about, as the protagonist Harry laments the literary talents he failed to develop to the fullest. As such, the leopard becomes a literary device that symbolically represents the idea of failing in the process of striving for great things, and so it also becomes the heart of the whole short story.