I don't know, but the rule makes perfect sense to me. Ordinarily you may want to study the video before you ask for a review, to conserve your percentages, but if the play ends the game, it is axiomatically true that an appeal improves the chances of the (otherwise) losing team, so there is no reason to delay, and you would have to appeal IMMEDIATELY. That makes perfect sense, and that's what the rule says.
Actually, I was at a game last night which ended on an appeal play. . .odd coincidence, but I was. Two out in the ninth, the Royals are down a run with a man on first base. They pinch run a fast man, Gore, but there's a pickoff play at first. Umpire rules him safe. Twins appeal. Twins win the appeal; game over.
By the way, VERY impressed with Byron Buxton. I just mentioned to my wife that we've been hearing about him since he was 18; he hasn't hit yet but he is really fast. A quarter of a second later he sliced the ball into the left field gap to the wall. MY GOD, is he fast! He's one of the fastest men I have ever seen.