It's a standard feature in nearly all common video editors (i.e. DaVinci Resolve or Adobe Premiere).

Usually, stabilization goes over all video frames and tries to find image transformations (rotation + translation + zoom) that make a frame match as closely as possible with the previous frame. That's an oversimplified explanation, but from a user point-of-view, these tools are mature enough to be applied with just a few clicks.

This video is definitely the result of that, as, whoever did it, didn't even bother to insert a cut when the feed switches between left side and right side camera, thus making the stabilization spazz out momentarily.