What makes the computer think this move is brilliant?

I just got one of my moves rated "brilliant" by the analysis engine for the first time.  It is move 69 in the following game, when I move my king toward the center in a rook versus pawn end game.  That seems more obvious than brilliant to me, so what is the computer thinking here?

Possibly of relevance is the wide swing in the evaluation around this time.  The preceding black move 68 is a blunder that changes the evaluation from +0.14 to +49.5.  The "brilliant" move preserves this +49.5 evaluation, so I suppose the change from the +0.14 after the previous white move might play some part in the computer's characterization of the move.  For others' "brilliant" moves, are they also associated with large evaluation swings?

Previously people have claimed that "brilliant" moves have to involve a certain depth.  I suppose that might be the case here, since the evaluation is probably based in large part on whether the pawn queens, which if it happens probably happens after a couple dozen ply at least.  Is this how the computer determines whether a move is "hard to find" - the computer determines a move is "hard to find" if it takes a deep search to find the approximate evaluation of the position after the move?

Also, two other questions about this game for those who might want to help:

- What happens if 68. ... Ke5 instead of 68. ... Kd5?  Why is the game not still won for white?

- Why is 67. Rf4 a mistake?

It is brilliant becasuse it is the only move that wins. The engine doesn't take the fact, that the move is quite obvious into consideration.

68..Ke5 draws as you have to move your Rook, and after that you will have to give up your Rook to stop the Black Pawn. The difference is that in the game your King is the important step closer. Endgames is often about one move. Try to play around and check it for yourself. It will be a god learning experience.

67.Rf4 is a mistake because you allow Black this drawn ending (with 68..Ke5). 67.Rf8 would have kept the winning advantage, as e.g. 67..Rxh7 68.Kxh7 Ke5 and again you can play 69.Kg6.

Is "only move that wins" different from "only good move", and how?  The analysis often says a move is "the only good move" but doesn't mark it as brilliant.

Thank you for the analysis of the other moves I mentioned.

Edit:  the mouseover for Brilliant Move is "the best move - and tricky to find, too".  How does the computer define "tricky to find"?

I guess it is programmed: only move = tricky to find. Wich is obviously not correct.