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HankronTo answer your initial question, you have, quite simply, an '1896 Baseball Table Game.' It was designed to be cut up, bent, folded and played by kids. It's a toy for kids.
Back in 1896, these sorts of paper/thin cardboard cutouts, punch-outs, scraps, paper fold-outs and such were extremely popular with little boys and girls. The 'baseball scrapps' punchout busts that are well known to baseball collectors is merely one example of this phenomenom.