Yes, this is exercise. Exercise can mean a number of things. It doesn't only mean an aerobic class or a treadmill. It means whatever you enjoy doing. It could be an aerobic class, gardening, sports, treadmill, stairmaster, walking, jogging, cleaning your house, swimming, taking the stairs, etc.
All physical activities require energy just like driving a car requires gas.
Back to our car analogy. Let's take a Ford Bronco and compare it to a Ford Pinto. The Bronco is big, strong and can do heavy work. A Pinto is small, fragile and is not meant to do heavy work, it's meant to get you around using the least amount of money. If both cars were left running for same amount of time, the Bronco would use more gas because it's stronger and needs more gas.