The story of Rikki-tikki-tavi appears as a section in Volume 2 of Rudyard Kipling's The Jungle Books. Epics typically deal with major events and Rikki's battle is described as a "great war" (compare Homer's Iliad, which deals with the ten-year-long Trojan War).
We find a heightened prose style in descriptions such as the one that occurs when Nag is killed by Teddy's father, whose gun "went off like a thunderclap just behind him; a hot wind knocked him senseless, and red fire singed his fur."
In this short story, Rikki, like many epic heroes, has a sidekick, Darzee, the tailor-bird (compare Enkidu, who helps Gilgamesh; or Robin who helps Batman).
Obviously, any encounter involving a serpent provides a thrill. Even today, it seems like everyone has a story about an encounter with a snake. The part of the story when Nagaina is waiting to strike Teddy's leg seems both suspenseful and thrilling.
The moral of good defeating evil appears numerous times in the story. Serpents are customarily symbols of evil in our culture. This moral, though, appears expressly in Darzee's song that he sings in honor of Rikki's defeat of the cobra: "Evil that plagued us is slain." Also, the fact that Rikki's deeds have inspired a song is also the mark of an epic hero (compare the song that the bard Demodocus sings about Odysseus in Odyssey 8). This song and several other ones heard earlier in the story also identify Darzee as the bard in this "mini" epic.