In OP's video example, that elephant's front legs are hobbled - that's when you rope or chain together (as in this case) a pair of legs to restrict an animal's natural range of motion, movement ability, and speed.

You can hear the chains rattle as the elephant moves, as well as see the hobbles, especially when the animal is close to the camera, like around 25 seconds into the video. The hobbles are causing this elephant to have an unusual gait.