I don't really understand how the technique described in the vimeo video makes the visual effect. It would have been nice to see what the camera is actually capturing and how it gets stitched together to form the final effect.
Take a picture. Put a light behind it and place a black mask on top of it so you can only see a vertical slit. Point a camera at it off-center. Open the shutter and pull the camera backwards, then close the shutter. You will get a long horizontal smear with the slit stretched out into a long foreshortened rectangle (it will be skinnier towards the center of the picture and fatten out towards the edge).
Now do the same thing, but as you pull the camera, move the picture past the slit horizontally. Now, instead of one 1d line being stretched out into a foreshortened rectangle, you are stretching a flat rectangle into a foreshortened one. To make a zoom effect, you do this several times (one for each frame) but with the background starting at different positions, so it appears to scroll towards the camera.
With a different shaped slit (a square or a circle for instance) you can make a tunnel sort of effect, like the Doctor Who sequence above. You can see the slit scan happening best at the top and bottom of the circular tunnel: notice that the texture is less detailed there and a bit smooshed. That happens because the circle is being dragged horizontally and at the top, the right semicircle and left semicircle are being dragged over the same parts of the background soon after each other. If you had a part of the slit that was totally horizontal, that part would come out without any 2d texture effect at all and would just look like a smeared out 1d line. So the circle is most detailed at the left and right side.
The whole tunnel has a sort of horizontally tilted feel, and that comes from the left-to-right (or vice versa?) dragging of the background.
