Unfortunately, they miscounted somehow: Jayson was only at 625 there. When you start a rack, there are 15 balls on the table. When someone told him he had beaten 626, and he celebrated by showing his bicep to the camera, there were 6 object balls left on the table, i.e. there were 9 balls in the pockets. There is no amount of racks plus 9 that adds up to 627 balls:

43 racks x 14 = 602

44 racks x 14 = 616

45 racks x 14 = 630

If he had missed the next shot, which he shot by stretching out diagonally on the table with a 30" bridge and poked at the ball, I think he would have been pretty disappointed.