Kipling's writing style is pretty kid-friendly. Everything from sentence structure to word choice is basically arranged to make things as accessible as possible. Here's an example:
Rikki-tikki smashed two eggs, and tumbled backward down the melon-bed with the third egg in his mouth, and scuttled to the veranda as hard as he could put foot to the ground. Teddy and his mother and father were there at early breakfast; but Rikki-tikki saw that they were not eating anything. They sat stone-still, and their faces were white. (87)
The sentences may be a little long by today's standards, but the flow and ease between subject and verb still make them accessible to all reading levels. The word choice remains on the safe side of simple. Sure, a child might have to ask what exactly a "scuttled" movement looks like and most houses don't come with a veranda these days, but these instances are few and far between.
That's actually the short story's stylistic advantage. A child learns these new words by asking an adult or looking them up as they appear. Since these more difficult word choices don't appear very often, the reader won't get frustrated by having to stop and question the meaning every sentence or so. This makes "Rikki-Tikki-Tavi" and excellent stylistic choice to build those reading muscles.