The UBA isn't really about baseball, although there's plenty in the book that baseball fans can relate to. The novel uses the trappings of baseball, the intellectual balances of the game, as a web for its protagonist to get caught in.
Let me back up a little. J. Henry Waugh is a loner, an accountant by trade, whose main obsession in life, at least by the time we meet him, is a tabletop baseball simulation. The results of the games are decided by rolls of the dice and a complex system of checks and balances. The design of the game is quite ingenious, given when the book was written (1968, years before today's Internet Sim Leagues).
Waugh's been at his league a while, and he's begun to give the game more added meaning by inventing backstories for his players, giving them personalities and beliefs. He imagines them congregating after the season in bars, playing golf tournaments, and entering politics. It's gotten to the point where the league is starting to interfere with his day job, and for a time, Waugh struggles to keep his league and his life separate. But a tragedy in the game finally irretrievably shatters the line between reality and imagination. He's created a world to take the place of his mundane existence, and becomes powerless to stop it from consuming himself.
There are most definitely religious undertones throughout the novel, from the protagonist's name to the last chapter of the book, when the theme becomes all too apparent. Coover's prose is sometimes maddening, but never boring. He takes us between reality and fantasy, and at times blurs almost unrecogonizably the line between them.