A different type of game. Based on breed abilities/adaptations, characteristics, and history (bonus points for obscurity)
I nominate the Catahoula Leopard Dog. But I am biased (that's my little girl, Daisy) First bred in Louisiana, and with a lineage as murky as the bayou waters they came from, these dogs have developed the ability to climb trees, webbed feet, and a deep chest cavity for bigger lungs/hearts for increased stamina, they were favorites of noted badasses Teddy Roosevelt and Daniel Boone. They're also one of the smartest breeds in the world. They're like if the local motors rally fighter and nissan gtr had a baby, and that baby was a dog.