The interesting thing about Kf1 is it allows Black two options.
1). Nd2+ spliting the K and R, to which White has the defense of Bxd2.
Which results in Black having a pawn on d2. Leaving White with the critical defense against the pawn.
2). Nxf4 which accomplishes several things. First removing the protection against the fork. and secondly threatening the Q.
White is left with two options, unless he wants to lose the Q.
Qxf7+ which grabs a pawn and supplies an insufficient threat to the K who retreats to f7. With the N protecting the critical g6 and h5 squares white will be unable to complete the mate. However gains a tempo allowing the R ook to move out of danger.
or Qg4 threatening to recapture the N.
In this line White will lose a R with Kf1