The “camera stabilizer” is an old trick, but a decent one.
Watching the video, note how the photographer holds the camera generally – palm up beneath the lens and body, elbows tucked in against ribs. (The video guy could have tucked in a bit tighter, I think.)
Also, photographers should learn to breathe properly (inhale fully, then let most of it out and hold breath during exposure), and to squeeze (rather than jab at) the shutter release.
The techniques for keeping a camera steady during exposure and keeping a rifle steady for an accurate shot are very similar.
G.