That looks pretty simple to me, they just took a picture of the same scene from slightly different angles (like move the camera a few inches to the left or right for each image) and then glued the images together to form a sequence (like an animated gif). Depending on how far the background is away from the camera, this will of course make the background dramatically shake because of the laws of perspective.
Obviously they kept the main object (the people) in the center of the frame, so that means if you move the camera to the left, the background will also move to the left in the final image. Try it for yourself by taking 2 photos of the same thing from slightly different angles.
EDIT: here's a quick diagram of what I mean, pretty crappy because I made it on my smartphone, but hopefully understandable.
On choosing the strength of the effect:
If the background is twice as far away from the camera as the object that you're keeping in the center of your image, the background will seem to move to the left twice the distance that you moved the camera to the left.
You can play with and tweak this effect by choosing the distance of your camera of course. Moving the camera further away and then zooming in the right amount, will keep the main object the same size, but will change the aparrent size of things in the background and also the strength of the effect above, if applied.