Some fish are just more aggressive and territorial than others. My plakat male is constantly on the move throughout the day, flaring at his neighbour, and patrolling the perimeters of his 'territory'.
As long as it doesn't seem to be causing stress to your fish, I wouldn't be too concerned. It's likely healthier for your betta to be active, than it is for your betta to be sedentary. After all, fatty liver disease is an issue that faces fish living in captivity.
He looks nice and healthy in the photos, so I say enjoy your feisty fish.