The original question had to be edited. Karin's role is significant. On one level, her imagination enables her to see the baseball game. When others cannot, Karin can. This helps to illuminate the transformational and redemptive nature of the game. Such a reality is intrinsic to the narrative. Due to her innocence and sense of purity, Karin becomes essential in conveying this.
Another role that Karin plays is to provide the pivotal movement for Doc Graham. Moonlight leaves the baseball diamond, transforming into Doc Graham. The game of baseball is shown to save human beings. The literal act of saving is something that Karin represents. When Doc saves Karin, it is a way to convey that baseball can save lives. It does this for Ray and for Salinger. It literally accomplishes this with Karin. It is for this reason that she plays a vital role in the story, clearly suggesting that with the young, the love of baseball will be immortal. Just as Ray's father passes this love to him, Karin serves to be the recipient of her father's love of the game. In a world where so much is destroyed and so little remains, Karin's presence reminds the reader that the love of baseball is one of the few testaments passed down from parent to child; eternal love in a world of mutability.