First of all, Enshin comes from Ashihara (Ninomiya was one of ashihara's top students), therefore the methods are essentially identical.
The video did a good job @ explaining the basic concept, but don't forget that karate isn't static. There may be several movements (back & forth, side-to-side, faking etc.) before the best opportunity to utilize one of the four directions for a specific attack/counter happens.
The primary goal of the tai sabaki (which I teach) is to gain maximum tactical advantage & be able to off-balance (kuzushi) -if possible- and finish the fight (sparring or SD).
Ed Ichihara Smith - Shukokai