A couple other things apparent in the video.
After the first strike, the pitcher receives the ball and stands on the pitchers plate, ready to begin his delivery while the batter is still speaking to the ump. The pitcher is still waiting when the batter steps out of the box.
After the batter steps out, the umpire motions toward the box three times while appearing to say something to the batter. During this time, the batter looks away from him and begins his deliberate routine of unstrapping and re-strapping his gloves.
After the umpire calls strike two, the batter continues to ignore the umpire and continues to fiddle with his equipment with the air of a man in no hurry at all.
Frankly, he looked like a petulant little kid making a show of not paying attention to his mom.
Then the camera cuts to the pitcher (a mistake by the TV production team because the action was clearly happening at home plate) and several seconds elapse before the umpire rings up the 3rd strike.
When the camera returns, the batter is still outside the box, having made no progress toward the box while the camera was on the pitcher.
It looked to me like the player was determined to show the umpire up for the strike call on the pitch, and then he was determined to show him he was the boss and couldn't be hurried along.
And the batter was absolutely right about who was the boss: he conclusively proved that the umpire could not make make him step into that box.