Black obviously is in bad shape and should be happy with a draw

68...Rxe5 does the trick, Now:

69.Kxe5 f6+ is stalemate irrespective of whether black captures the pawn or not

69.Rxf7 Rd5+ 70.Ke6 Re5+ and so on with a draw

69.Any other rook move apart from Rxf7 Rxf5

At my very first glance, I thought it was white to play, and I was very concerned that the black king was almost stalemated, and, that given half a chance, black would try a "crazy rook" maneuver in order to achieve said stalemate.

At that moment I noticed that it was black to move and started typing this.

It seems that the correct move is, indeed...

68...Rxe5!

If white captures the rook with 69 Kxe5 then 69...f6+ draws by stalemate. White's best try seems to be

69 Rxf7

Now black can start checking the white king until he gets sick and tired and agrees to the draw (or takes the rook, resulting in stalemate). Eg:

69...Rd5+ 70 Ke7 Rd7+ 71 Kf8 Rd8+ 72 Ke7 Rd7+ 73 Ke6 Re7+

Uh, oh. If white doesn't want to lose he has to take the rook

74 Rxe7

Stalemate.

Hiarcs says it is good enough (+3.79, 25 plies deep), but perhaps not trivial OTB.

I guess the idea would be to advance the e- or f- pawn forcing an exchange, then hide white K from checks and promote...

After 68.Ra6+:

It may have been the last move before the second time control, which is often at move 60.

If Black then tries the stalemate trap with <68...f6?> (hoping for 69. e6 or 69. exf6) White replies <69. Re6!> and wins, e.g. 69...Rxe5+ 70. Rxe5 fxe5 71. Kd5 1-0

68 ... Rxe5
69 Kxe5 f6+

which forces the stalemate.

But in fact, white will not do this if he plays best. White will move the rook in response. But he will not take grab back the pawn, because of

69 Rxf7 Rd5+

Here white cannot take the rook which results in the stalemate, so he has to evade the check. If he moves to the queen side, then the rook just follows resulting in perpetual check.

It is possible for white to try and get the king to the other side of his rook, which is the line

69 Rxf7 Rd5+
70 Ke7 Re5+
71 Kf8 Re8+

which forces the king to take the rook resulting in the stalemate.

The king can also try and end the perpetual checks in front of the rook

69 Rxf7 Rd5+
70 Ke7 Re5+
71 Kf6 Re6+

here white is forced to take the rook either with the king, or the pawn. But this ends up in the same old stalemate.

So what's white got? Stuff like

69 Ra8 Re4
70 Rg8 Rxg4
71 Ra4 Kxf7
72 Ra7+

which is perpetual check.

There are probably other lines. I couldn't find any answer for white that wins, and don't really think black can turn the tables either. So I checked with Rybka and it sees a draw.

Because 61.f6+ puts Black's King in a bind and White gets the pawn back. For example,

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