Jane's keeping her kings in the back row is symbolic of several things: first, it's a refusal to play or win the game. Jane is refusing to grow up, and Holden likes this. Second, it's non-threatening; it suggests the game can go on forever. Holden is confused by adult women (who threaten his childhood). He wants to remain in childhood forever, and so he adopts her strategy. Third, it could represent sexual repression. She wants to stay a child (virgin) forever.
This all relates to her stepfather, whom we are led to believe has abused her either physically or sexually. In response, Holden kisses her all over the face, but not her lips. This is a sweet, childlike act devoid of sexual advance. Holden wants to wash away Jane's sexual abuse with kisses without threatening or arousing her with a kiss on the lips.
Jane is a girl whom Holden finds unique and attractive. He fondly recalls some of her idiosyncrasies (like how she played checkers). Holden is attracted to her and respects her, unlike most of the other people in his life. Throughout the novel, Holden expresses his desire to see her and talk with her, in the same way he does with his younger sister (Phoebe), whom he also respects. Holden is furious when he finds out that his roommate Stradlater also likes Jane. He wants to talk to Jane about it, but he is paralyzed when he thinks about really doing this. This shows that while Holden desperately wants to stay connected to people in his past, he is always afraid that they will let him down. Holden is depressed and his constant vacillation regarding what he wants to do or thinks he should do and what he actually does do exacerbate his fear, sadness and self-loathing.