In general, Rikki-tikki is a threat because he is in the same habitat as Nag and Nagaina. A mongoose is a predatory animal, so Rikki-tikki is capable of efficiently killing another animal. Additionally, snakes are a typical prey species for mongooses to hunt. Rikki-tikki is a threat to the snakes because of a basic food chain hierarchy.
Nag and Nagaina definitely feel the potential threat that Rikki-tikki represents once Rikki-tikki proves he is more than capable of dealing with a snake. First, Rikki-tikki proves his quickness by dodging Nagaina's sneaky attack from behind. Second, Rikki-proves his ability to kill when he kills Karait.
The final way that Rikki-tikki is a threat to Nag and Nagaina is that a mongoose is an opportunistic predator. A mongoose survives by hunting many different prey, which doesn't bother the snakes. What does threaten the snakes is that a mongoose will often raid nests and eat the eggs. Nag and Nagaina have chosen this particular yard to lay their eggs and raise their young. Rikki-tikki not only threatens the adults, but he also threatens the lives of the unborn snakes.