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.
Or, if black takes the N on move 4:
Of course, black can give up the Q to avoid mate in some of the lines below. But, assuming he doesn't:
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.