Gravity is not the only force that affects the motion of an object falling toward Earth. When an object moves through the air, air molecules push against it in the opposite direction with a force called air resistance. When forces act on an object in opposite directions, they counteract each other. As a result, air resistance reduces the effect of gravity and therefore affects how fast the object falls.
As you saw in the video, when an astronaut on the Moon releases two objects at the same time from the same height, both objects accelerate at the same rate and hit the surface of the Moon at the same time. This experiment would not have the same result if it were done on Earth because of the air in our atmosphere. But because there is hardly any atmosphere on the Moon, the only force acting on the objects is the Moon's gravity.