The rule you cite appears to cover the situation when the pitcher starts and then stops the pitching motion or completes the motion but does not throw the ball.
It is not explicit here, but it does not cover the situations where the pitcher begins a motion to throw to another base. Other rules (such as 6.02(a)(3) and 6.01(a)(4)) cover them.
In the video linked, the pitcher is in position on the rubber, picks up his forward foot, turns, and steps directly toward second base. This shouldn't be seen as violation of 6.02(a)(1).
Feints are specifically mentioned and not disallowed when the motion is to second base, so I see no reason for this to be a balk.