No the mites will not live on your cat. They are host specific, living only on snakes.
In the wild, snakes have way more room to roam around. The mites don't have a chance to breed to much.
In captivity: a few mites get into your cage. The conditions are good (stable, high temp) and there is readily available lunch always 2 ft away. Nothing ever comes to kill the mites or eggs. The mites continue to multiply and settle in on the snake.
In the wild: a few mites get together in a colony. Some get wiped out by wind, some by cold or rain and others by predators or starvation. They spread out, breeding, but not in great numbers in one concentrated area. A snake picks up a couple when it's sleeping or moving, but thats it.