What animals, besides humans, exercise recreationally for personal benefit?
Pretty much any mammalian predator, mind you they don't exercise the same way we do.
For example; bear cubs, lion cubs, wolf pups, dogs, and cats routinely play fight with one another. This allows them to hone/maintain their skills as well as build muscle mass and balance/dexterity.
If they do not do this, they will be poor hunters and not be able to break down proteins and fats adequately. They may even randomly sprint or climb objects within their habitat.
But they do not do this for vanity, and the end of the day it is strictly survival.