Well, first off, your Title was a bit misleading. She is suing the Gap because the company's marketing team chose to find a look alike of her, have her styled similar, and in a very, VERY small way, imitating her.
Kim has no other way to support herself besides media appearances, doing adverts, etc. Its a different situation than if they had imitated someone like Marilyn Monroe, Elvis and the like. She makes her living off adverts, so gap essentially paid for a generic brand of Kim.
Wanting to get advert money for the girl even styling herself as a look alike is a bit far, and probably wont get well off in court, but you can see the similarities.