Not really. After the third out is made and called the players all leave the field.
The batter in this play himself had done it. He started to his dugout the other way.
The whole thing in ludicrous. He would be out for running outside the base line if this really were a dropped third strike.
That is absolutely not true. Some people on this thread are woefulling uninformed about what constitutes when "running outside the baseline" is against the rules. They would call a runner out for rounding first base on a double. Or for sliding past home plate on a close play and then scrambling back to score if the tag was missed.
AIt's been awhile, but as I recall, the batter is not out automatically until he enters the dugout.