I believe that simply creating emotional experiences in a game is its own reward, in the sense that it makes the game more engaging and rich.
It's even better, however, if the emotion can be used to influence the player's actions and decisions within a game.
Take the previous example. If you find that the female alien is actually terrified of you and you need her help on an important quest but are afraid she might desert you out of fear then you might need to take some kind of action in the game (go off on some mission) against an evil and dangerous enemy of hers to prove she need not fear you.
Perhaps, for instance, the technology in her ship is of great interest to your military superiors. They want to do a raid on her planet to capture some of this technology. Only by stopping them do you regain the woman's trust. She, in turn, is now willing to help you, which forwards the game.
The point is that the emotions you feel for her trigger action. They triggered your defending her from your partner, and they can trigger other actions as well. Emotion thus feeds into plot and gameplay.