That sure doesn't sound right. Player 1 of a 2-player game should have the same playing experience as on a single-player game.
Based on the flyer, we can see that the game counts strikes, which is very unusual for a pitch-and-bat game. The flyer doesn't say so explicitly, but the depiction of innings on the backglass probably means that the game is adjustable for, say, 1-3 innings per game. You could look for an adjustment for number of innings, try different settings, and report your findings here.
You'll need the schematic to get all the details about how outs and innings are handled on this particular game.
.................David Marston