Vaughn was a starting pitcher for them, Lou says it's Vaughn's turn in the rotation but made a call to start Harris instead because of Vaughn's struggles with the Yankees he went with someone else.

Okay, that makes sense in regards to the number of games. But it leaves the rotation question open. Wouldn't the rotation schedule still have been known, prior to the bus trip on the way to the game?
And if the other guy wasn't always the intended starter for that game, does that mean he was put into that role out of rotation, thereby denying him a proper rest period? That seems to be more important than his experience against the Yankees.
Also, why does it matter about Vaughn not starting against New York? Isn't he a closer? So, wouldn't he already know he's not starting?

There was a day and age before wildcard games etc. where the team with the best record in each league would play the World Series. Since, in the movie they end the season tied, it was a one game play-in game