'Static' computer evaluations tend not to mean terribly much. Picking on a move like this means there's a reason. Not always a good one but fun to unpick the (twisted) computer logic whatever
I'm not totally sure about this being strictly right as its based on a bunch of rook endings. Computer aren't great at evaluating those and I'm no doubt quite a bit worse....
Of the moves: Even thinking of 1.. Rf5 clearly shows carbon based thinking as white can just play Rxf5

1 .. g5 probably should be in range of humans too as white can go 2 Re1e3 Bxe5 3 Rxe5 Qxf3 4 Rxg5.
1... Kh7 is more forgivable. The problem there is that white can go 2 Re1e3 and meet 2... Bxe5 with 3 f4 Qg4+ 4 Rg3 Qxf4 5 Qxg6+ Kg8 6 Qe6+ Qf7 7 QxQ+ RxQ 8 PxB etc. 'Obvious'....
So maybe 1.. Rf6 is a waiting move to prepare for 2 Re1e3.... After 2 Re1e3 Bxe5 3 Rxe5 Qxf3 4 Qe2 QxQ 5 RxQ you can go Kf7 and the rook is very well placed for the ending with f5/b6 to pick from. Much better than on f8.
The most likely horizon effect candidate would be that 1.. Rf6 2 Qd2 g5 wins. Takes my comp a few moments to work through that. No wonder really - after 3 Qxg5 you have to go 3.. Bxe5 4 Rxe5 Qxf3 or 4 Pxe5 Rh6. Not clear cut wins.
I spent a while rather puzzled why it felt that 1 .. Rf6 2 Qe2 Bxe5 3 Qxe5 Qxf3 4 Qb8+ Rf8 5 Qg3 QxQ+ 6 PxQ was a non trivial improvement on 1.. Bxe5 etc. That's actually the same position except for whites f2 pawn being on g3. However the clear second rank means that 6 .. Rf6 7 Re5 Rb6 8 Rxd5 Rxb2 9 Ra5 a6 10 Ra4 b5 is now winning due to the b4 breakthrough. So white has to defend a bit more passively instead. Its a seriously hard game sometimes
