It is indeed 1.Bh7! not only with the skewer threat but the opening of the e-file, which results in mate if black tries to save the Q.
[FEN "8/6p1/4k2p/pp6/1B1bB2P/3N1P2/q5P1/2R4K w - - 0 1"]
1. Bh7 Qa4 2. Nf4+ Ke5 3. Re1+ Be3 4. Rxe3+ Kf6 5. Re6+ Kf7 6. Bg6+ Kg8 7. Re8#
Or, if black takes the N on move 4:
[FEN "8/6p1/4k2p/pp6/1B1bB2P/3N1P2/q5P1/2R4K w - - 0 1"]
1. Bh7 Qa4 2. Nf4+ Ke5 3. Re1+ Be3 4. Rxe3+ Kxf4 5. Re4+ Kg3 6. Be1#
Of course, black can give up the Q to avoid mate in some of the lines below. But, assuming he doesn't:
[FEN "8/6p1/4k2p/pp6/1B1bB2P/3N1P2/q5P1/2R4K w - - 0 1"]
1. Bh7 Qa4 2. Nf4+ Kf7 3. Rc7+ Kf6 4. Rc6+ Ke5 5. Nd3+ Kd5 6. Be4# *
[FEN "8/6p1/4k2p/pp6/1B1bB2P/3N1P2/q5P1/2R4K w - - 0 1"]
1. Bh7 Kf6 2. Rc6+ Kf7 3. Bg6+ Kg8 4. Rc8#
[FEN "8/6p1/4k2p/pp6/1B1bB2P/3N1P2/q5P1/2R4K w - - 0 1"]
1. Bh7 Kd7 2. Bf5+ Ke8 3. Rc8+ Kf7 4. Rf8#
[FEN "8/6p1/4k2p/pp6/1B1bB2P/3N1P2/q5P1/2R4K w - - 0 1"]
1. Bh7 Kf7 2.Rc7+ Kf6 3. Be7+ Kf7 4. Bg5+ Kf8 5. Rc8+ Kf7 6. Bg8+ Kg6 7. Rc6+ {winning the K instead} Bf6 8. Nf4+ Kf5 9. Rc5+ Qd5 10. Rxd5+ Be5 11. g4#
Ok, blah blah blah, all those variations. The bottom line is black's K is much more danger than is first apparent. The opening of the e-file is that little extra something that pushes things over the tipping point.
In the game, Spassky managed to beat Geller with 1.Rc6+ but it obviously took longer.