1) Since it's an all-star team, I'm guessing it's composed of above average players. Rex was in the game for the last possession, so that speaks to the confidence the coaches had in him.
2) Since the game was tied or close at the end, I'm guessing Rex's coach called a timeout just before that possession. It's hard to tell from the video, but it appears Rex was the decision maker on whether to shoot or pass it off. That too says something about the staff's confidence in him.