1...kb7 2. kf7...Rf2+ 3. Kxg7...Re2 4. Kf2...Rf2+
Here, black alternates the rook between the e,f, and g files depending on the position of the white king. if Ke8, Rg2 to attack the g pawn. if the white king to the f file, then Rf+. If the white king to the g file, then Re2 attacking the e pawn. White cannot make progress
4...Rf2+?? is the losing move for Black in your diagram, and the rest just shows White's win.
4...Kc6/c7 are the right moves there, and if 5.g7, 5...Kd6 seals the draw as in the OP's puzzle, i.e, 6.g8=Q Rf2+ followed by 7...Rg2+ and 8...Rxg8 and the e-pawn will fall anyway.
I thought the concept behind this endgame was interesting: