He doesn't have to loose the rook, white can also play for a draw. After taking the rook black has a pawn more but the king is more active. White will either lose or draw so I dont know if 2Kf4 is really the best move?
However, note that "The goal of Chess Tactics is to gain maximum advantage in the shortest possible number of moves." Yes, white could quickly force a draw but that is better for black than a prolonged game ending in a draw. I can't work through all the possible permutations and combinations to see if either side will eventually win, but I suspect the computer is not too far off the mark.