I think that you're supposed to move your rook continuously from a1 to a6 and it will be a drawn R+K v R+K endgame.
Rook Trick

Yep. Move your rook down to a6, then when the White king moves up to attack it, play back down to a1. As soon as White plays Kb6--thus threatening to move his rook and queen the pawn--you check the king away.

You see, if Kd7, then Rh8, Rxa7, and Rh7+! skewering the rook and king. If he attacks your rook, just move it. It didn't talk about if the king tried to take the rook.

if white is within reach of defending the pawn with his king you must bring your rook all the way back to a1 or a2. then if he touches his pawn with the king you give check to him on the b file then bring the rook back to the a file

Btw OP you might well find the following link of use (I know I do). It's good for any position at all with 6 pieces or less (and will show you all possible moves and variations):
http://www.k4it.de/index.php?topic=egtb&lang=en
I am reading a book, How to Beat Your Kids at Chess that says "Black to move draws by 1.... Kg7!. The black king simply toggles back and forth between g7 and h7."
When I tried that against my son, however, he just moved the king on g2 over and took the rook in 6 moves. Not a draw. I suppose that I could have moved the rook up to a6 as the king approached, but I don't see how I get a draw from that. What am I missing?