Your heel doesn't have leverage to lift your body off of the ground. If your heel is leaving the ground it's either your knee lifting it or your toes pushing it. In the gif you linked, and in proper running form, you push with the balls of your feet. Your ankle / heel system is solely a fulcrum that doubles as a dampening spring.
"pushing" isn't the only way to apply force. from the gif the ball of the feet start and end the "pushing", but this is unrelated to how much lifting you do with the heel