I highly doubt any player never moves thier head a little at times......You can force a still head over and over 100 times but under pressure on certain shots your body will do "naturally" what it needs to do to compensate.......of course ideally you want no head movement........I am sure there are certain shots where SVB moves his head and also Fedor...Efren, Earl, Segal...go right down the line and you will find some head movement from time to time.......The head movement most likley will come from a change from the normal shot....perhaps a power shot causes it when the stroke gets lenghened out.....many many variables..... but the root cause of the movement will be due to grip, stance and posture....(for that shot)
What I am referring to is most pronounced at 2:16:40 of your video you posted...you do it many other times but it is always going to happen based on your grip and stroke....The cue is not going back level...it is what I refer to as a see saw type stroke.....It is subtle but you can see it in the tip as well on many shots.....If the cue is going up on the back swing.....so must your head (naturally follow)....try and keep your head still and your whole upper body will move to compensate.
Here is an example video of Shanes set up and takeaway....notice the cue drops down on take away...and (For the most part) his head and upper body stays still)
I see multiple ways of fixing this....change your grip so that the stroke on takeaway at least stays level or drops away from the chin......Or if you are comfortable with the see saw stroke (there are players that play like that)....Adjust your posture a bit so your chin starts off the cue instad of on it.
Your choice.......Of course this is just one persons observations from watching your video.....Good Luck!!!