What is so impressive about this trick is the speed with which the water drains from one bottle to another once you've created a whirlpool.
Try draining the water from one bottle to the other without spinning them – you make very slow progress as both the air and water battle to get through the small gap at the same time.
By spinning the bottles you create a whirlpool which has a hole in the middle of it, in fact you can look down onto your whirlpool and see a tunnel right the way through the centre.
The air can now travel up through this hole, while the water drains down around the sides. As they don't have to compete for space, the process is speeded up immensely.
There's a myth that because of the Earth's rotation, water always goes down the plughole in a clockwise direction in the northern hemisphere and anticlockwise in the southern hemisphere.
The Earth's rotation does affect the direction of circulation for large bodies of fluid, such as atmospheric storms or oceanic currents, but in your bathroom it's the shape of the basin, or the movement you generate as you take the plug out that causes the water to spin in one direction or the other.