Seems that Ree1 is the only winning move here. Does your engine agree?
Here is the game:
1. e4 Nc6 2. Nf3 a6 3. d4 g6 4. Nc3 Bg7 5. d5 Ne5 6. Be2 Nxf3+ 7. Bxf3 Nf6 8.e5 Ng8 9. Bf4 d6 10. Qe2 Bf5 11. O-O-O dxe5 12. Bxe5 Bxe5 13. Qxe5 f6 14. Qe2 Qd6 15. g4 Bd7 16. Qe3 h6 17. Ne2 f5 18. gxf5 Bxf5 19. Nd4 Nf6 20. Nxf5 gxf5 21. Rhe1 Ng4 22. Qd4 O-O-O 23. Bxg4 fxg4 24. Qxg4+ Kb8 25. Qh4 Rhf8 26. Rxe7 Qc5 27. Ree1 Qxf2 28. Qxh6 Rh8 29. Qg5 Qxh2 30. Rd2 Qd6 31. Kb1 Qb4 32. c3 Qd6 33. Ka1 Ka8 34. Qe3 Rh4 35. Qg1 Rh5 36. Red1 Qe7 37. c4 Qb4 38. c5 Rf5 39. a3 Qc4 40. Rc1 Qf4 41. Rd4 Qg5 42. Qxg5 Rxg5
[d] k2r4/1pp5/p7/2PP2r1/3R4/P7/1P6/K1R5 w - - 7 43
43. d6 Rd7 44. b4 Rg6 45. Rcd1 Ka7 46. Kb1 Rf6 47. Rd5 Rg6 48. Ka2 Rg3 49. R1d2 Re3 50. Kb2 Re1 51. Kb3 Re3+ 52. R2d3 Re1 53. Ka4 Re2 54. Ka5 Re4 55. dxc7 Rxc7 56. a4 Ree7 57. Rd8 Re2 58. R3d5 Rce7 59. Rh8 Re8 60. Rh7 R2e5 61. Rdd7 Rb8 62. Rdf7 Rg5 63. Rc7 Ka8 64. Rhf7 Re5 65. Rcd7 Ka7 66. Rd6 Ka8 67. Rg7 Rf5 68. Rdd7 Rh5 69. Rdf7 Re5 70.Rc7 Rh5 71. Rce7 Rf5 72. Rh7 Ka7 73. Rc7 Ka8 74. Rcg7 Re5 75. Rf7 Rg5 76. Re7 Rd5 77. Kb6 Rd4 78. b5 Rxa4 79. Rxb7 Rxb7+ 80. Rxb7 Rb4 81. Ra7+ Kb8 82. Rxa6 1-0
[d] 1k6/8/RK6/1PP5/1r6/8/8/8 b - - 8 82