I don't really believe such thing as unnessecary movements exist. The body always does naturally what serves the movements your hand and fingers do naturally. There's not really one wrong intuitive mechanical approach to a given sequence of notes since the body does not work inefficient by nature, and this is reflected in the infinite varieties of possible ways to play that given sequence; and i'm not even referring to anatomical differences or differences in articulation.
But this is probably not the best place to discuss our opinions on piano&anatomy anyway. 
You sound like you've studied Alexander Technique. Alexander's theory was that we are all born into natural movement, and movements rise out of unadulterated "purposes" ("I am going to lift my leg above this chair") that ensure the pureness of the movement itself. But if you did study it, or if not, you are still neglecting the second part of his thesis, and that is that we learn throughout life all kinds of other motions which are hindrances to pure action. We learn them through observing others in our society, or because of injuries which put is in a certain habit of action (moving in a certain way to avoid pain, even if the pain has passed), etc. In short there are all kinds of accumulated movements that are not necessary to our goals, and this is especially true in musical purposes.
As a child, I often lifted my fingers very high, and especially made them splay out in certain passages where I wanted to highlight single notes. This was born from my desire to make a passage expressive in a certain way, to speak in the most general terms. But those motions are not necessary. All that physical activity, the strain on the fingers, the ultimately absurd-looking gesture, is just a waste of energy, a spreading out of energy that should be distilled and focussed inexorably on the production of music, not going this way and that.
You may have an excellent technique, and perhaps this leads you to say, "just be natural." But those with excellent techniques always forget that the most complicated figurations had to be learned, sometimes easily, sometimes painfully, but they always had to be figured out.
Through my own experience, watching this video, I can honestly say that I believe most of the movement excess to the production of sound is unnecessary. It's unnecessary from the point of view of producing the music, and it's unnecessary from the point of view of expressing the music publicly. To me, perhaps as a result of my training, it looks like the energy that should go straight into the keyboard is going in all different directions. As a listener, I'm distracted, and the full effect of the music is lost. If I closed my eyes, I may not feel the same way. But then again, he posted a video, not a sound file.
Walter Ramsey