"Let it rest" is advice for cooking large cuts of meat in one piece, especially if it's desirable for the end result to be on the rare side. So steaks, roasts, pork tenderloin, that sort of thing, you want to let the meat rest (== cool down) so that when you slice into it, you don't get a huge puddle of hot juices all over your cutting board, and no tasty hot juices in the meat where you want it.
Note that this doesn't depend on the type of meat, only on the desired end result. For an analogy, consider bread dough. Sure, you can cut it into little pieces and fry or bake them up individually, but that doesn't make bread, it makes fried dough or dinner rolls. (Mmmm... now I crave lángos.) If you want bread, you need to bake the dough in one piece, and then let it cool down before you slice it so you don't end up with a gummy mess.
The Teppanyaki chef is making the meat equivalent of lángos (= fried dough). Apart from using the same ingredients as a steak, it's a completely different dish.