puzzle 10619: ridiculous

After the initial moves 1.Bxf7+ Ke7 2.Qe2+ Kf8 3.Bh5+ Nf6

4.RxNf6+! curtains:
a) QxR 5.Qe8#
b) gxRf6 5.Bh6+ Kg8 6.Qc4+ with mate in 2

instead the intended "solution" continues with 4.Nc3 and some random moves

Well, it wins a pawn at least

What about c) Kg8

c) Kg8 Qc4+ seems to be mate in 2, i'm not that good at chess/puzzles :)

c) Kg8 5.Qc4+ looks like mate in 2 also, no?

=> so we don't talk material but mate...

When playing against the computer it replaces Nf6 with Nf4+, maybe the server generating the puzzle was using its power for something else and missed stuff? I can't seem to find anything wrong with 4.RxNf6+! leading to mate but the puzzle is missing that line.