Okoye: Guns... so primitive.
Everett K. Ross: You're telling me that the king of a Third World country runs around in a bulletproof cat suit?
Ulysses Klaue: Why don't you ask him yourself? He's right outside this very moment.
Ramonda: My son, it is your time.
T'Challa: What happens now determines what happens to the rest of the world.
Ulysses Klaue: Tell me something. What do you know about Wakanda?
Everett K. Ross: It's a Third-World country. Textiles, shepherds, cool outfits.
Ulysses Klaue: All a front. Explorers have searched for it, called it "El Dorado." They looked for it in South America, but it was in Africa the whole time. I'm the only one who's seen it, and made it out alive.
Answer: Zuri feels guilty for his role in the death of Killmonger's father, which is why he tells Killmonger to kill him instead of T'Challa. While Zuri himself probably doesn't actually want to die, I don't think he wants Killmonger dead either, which is why he wouldn't kill him. Also, as a royal advisor, it would probably be looked down upon by the other tribes if he violated the rules of the ritual combat. After all, one combatant has to defeat the other in order to rightfully claim the throne.
Phaneron ★
Zuri may not want Killmonger to die, but he knew that the duel would only end once one of the contestants would either surrender or die, meaning Killmonger would stil win or kill T'Challa. It seems a rather low price to be looked down upon or fired if it means your country doesn't go to war. At least, that would be a small price to pay for keeping the peace.