That sample looks like a creative use of removing of an I frame in the stream.
Not sure how familiar you are with video encodes, but a stream is frequently comprised of I, P, and B frames. I frames are intra frames, or whole pictures, P frames are predictive, and B frames are bi-predictive.
Only I frames are whole images, with P and B frames being partial image chunks that move according to the pixel vectors in the encoded file. That is, the encoded file compression calculated what direction the pixels were travelling in, and uses those smaller chunks to save space by moving smaller portions of the image around instead of using a whole frame. Over time, smaller pieces might be updated because they have changed significantly from the original I frame.
When we strip out the I frames, we end up with the motion vectors telling the decoder to move the same area of the image. However, without the I frame, it is moving chunks of the previous shot, as with your example. Slowly, over time, some of those pixel vectors are updated with newer image chunks, hence why the dog gradually appears.
How to replicate this in Blender is no trivial task. If you were to track the entire scene, using many hundreds of points, you could possibly achieve a similar effect by gradually transitioning portions of your image from the first shot to the second. That is, assuming you have shot A and shot B, you could use a tracked version of shot B to gradually transition in portions of shot B over time. Coupled with shot A being a simple subdivided plane, you could possibly shape deform it based on shot B's tracked points. If the tracked points used smaller, geometric shapes, slightly blurred, you have the basis for a general transition by fading in portions over time, until the entire image is replaced.
Shooting from the hip, but that is a loose approximation as to what the datamoshing trick does in your sample.