That "fat labrador bounding" (pretty accurate description lol) is unfortunately not a natural motion but is caused by this elephant's front legs being hobbled together by chains. Example pic of chain hobbles on another elephant.

In OPs vid, you can hear the chains rattle and see them connecting the front legs together as the animal moves. Trying to run while hobbled is what's causing the unnatural 'bounding' gait pattern of this elephant.