Going into the river, there are 10 BBs in the pot. After the bluff-raise, there are 13 BBs in the pot, so the pot is laying 13:1 for the SB to call. He needs to be good 7% of the time to make this call. Given that there were two busted draws after 4th street, AA and KK has to call for 1 bet. This is a pretty standard call in the 10/20 SH games, I think.

Beyond this, the author's read distinctly left open the possibility of hands like AQ or a boat. The previous action does not justify a bluff-raise on the river here, as your only win is to re-bluff somebody who has overplayed KJ or AK. Had the author left open the possibility of a sickeningly overplayed small pair like 55, I would agree with the bluff raise, but basically you can't make this move except against a maniac. It really makes no sense here against a TAG.