Instead of two chess games or two different brains overlooking the same game.  It could also be that the "spacio-temporal" split of Terra/Antiterra could simply be simply a split in consciousness,  Van's.  He could well be the psychotherapist drawn into madness by the "texture of time" that is so palpable for his patients.

[...]Incongruity is spacio-temporal... We could approach this description to another that arrives two paragraphs later: "two chess games with identical openings and identical end moves might ramify in an infinite number of variations, on one board and in two brains, at any middle stage of their irrevocably converging development" (A,18). There is an assertion that a "sliver of light" of infinite variations lies between the "darknesses" of definite beginnings and equally determinable endings. This might be as true for chess matches as for the convergence of the "parallel" spaces of Terra and Antiterra - should we accept that these two chess games, or characters, represent a single one, now doubled because it is apprehended by the two different brains that are exercising themselves on only one board. Reader and book. Past and present...