That part of the story is suspenseful for sure; however, it is oddly suspenseful. It's odd that part is suspenseful because readers get no details of the underground fight that ensues. Essentially, readers are told Rikki-tikki went in the hole and came out alive. That shouldn't be suspenseful, but it is.
The reason it is suspenseful is because Kipling uses the most suspenseful technique of all: the unknown. The unknown is scary because our imaginations take over. All Kipling does is feed those imaginations with small, hinting details. As Rikki-tikki plunges down the hole, we are told a mongoose should never choose to do that. The underground passage is the snake's home territory. Nagaina knows all the ins and outs. Rikki-tikki is fully aware that he has no idea when the passages will open up and allow her to strike. By this point in the story, readers are accustomed to Rikki-tikki being in control and almost fearless; however, that is not happening at this point. Readers realize there is a very good chance Rikki-tikki made a fatal mistake. That's suspenseful.
It was dark in the hole; and Rikki-tikki never knew when it might open out and give Nagaina room to turn and strike at him.
Kipling then forces the reader to wait. He does not announce the outcome of the battle in the next paragraph. Instead, Kipling has Darzee start announcing Rikki-tikki's death. That brings even further doubt into the minds of readers. Considering that the entire "hole" sequence is about a paragraph and a half, it is very suspenseful.