My BlackBerry Q10 behaved the same way and I think my older Nokia E7 also showed similar results when taking pictures at speed. I noticed that on my 1020 too. While I can't explain why this happens, I think it is a more or less common artifact for mobile phone camera modules.
The Lumia 1020 has what is called a "Rolling Shutter", ie it draws the image on the sensor in lines.. Hence when you are moving, the image gets drawn in lines that warp as you move