As a geologist, I hate to burst the bubble, but what you are seeing is the dog sensing the seismic P-Waves which are compressional waves which move at twice the speed as the surface or S-Waves.

Since the P-Waves are compressional, you cannot see any visual evidence of them because the occur in a bump-like manner. The latter S-waves are longitudinal waves that you can see in the video. The time gap between the P and S Waves is how we determine the distance from the epicenter. Triangulating those various distances is how you determine the epicenter location and depth.

It's not that they can predict an earthquake, rather they can sense P-waves that many times we ignore or think are something else.