Kratos motivation is hate. Hate for himself, hate for the gods and contempt for everyone else. It's the only thing that keeps him going through most of the games. I don't think that makes him one dimensional or underwritten. It's just the only thing he has left, the only thing that keeps him want to live. That makes him a rather unique character.
“It appeared that there had even been demonstrations to thank Big Brother for raising the chocolate ration to twenty grams a week. And only yesterday, he reflected, it had been announced that the ration was to be reduced to twenty grams a week. Was it possible that they could swallow that, after only twenty-four hours? Yes, they swallowed it.”
- George Orwell, ‘1984’