He's more of a metaphorical king, in the sense that the T-rex was the King of the Dinosaurs, or Elvis was the King of Rock, or various animals are the King of the Jungle.
Donkey Kong is an animal rights activist, a vegetarian (only eats bananas), a loving father, and a working class hero. He fights King K-rool who Game Theory argued is a standin for Teddy Roosevelt and the Banana Wars.