Achieve a video warping effect, where it appears like the camera was shifted
This particular effect couldn't be done without some pretty advanced computer vision algorithms and a whole lot of processing.  Based on the screen shot alone, it appears that it tries to identify flat surfaces and objects within that space so that it can alter the camera's perspective.

Note that this is quite imperfect as you have no material for the actual side of people's heads and such.  Additionally, you can see that the system they were using doesn't understand transparent objects well.  It saw the net as a wall and modified it differently from the court, which is why we end up seeing that disjointed line where the net is.

I'm not aware of any specific system that does this, but I wouldn't expect it to be cheap and I really, really wouldn't expect it to be free.

If you don't care about cost, the fundamental start to it would probably be something along the lines of SynthEyes, as long as the camera does move some.  This can track where the camera actually moved and use that data to establish what depth things were at and what backgrounds looked like.  From that, it may be possible to create a virtual scene which you can effectively move the position of the camera in.

If the shot isn't moving, then I couldn't find any tools that would be helpful and your best bet might be to try contacting the company that produced the video directly to ask them what they used.  It appears to be something very specialized and not particularly well advertised as far as I can tell.