It seems like you're discussing a situation other than this case, but I can't figure out what it is. The court ruled that Gawker unlawfully invaded someone's privacy. They are clearly in the wrong no matter how you look at it. This isn't a case of rich people abusing the court system or using money to gain an unfair advantage. This is justice being done in the service of revenge, which is the usual way in which justice gets done.
I'm going to stick by the idea that people can use their money however they want within the boundaries of the law. The idea of not making powerful enemies is sound because there are countless ways that someone can use resources to make life difficult for someone else. It would be impossible to outlaw all of them, and you wouldn't want that even if it could be done.
I'd still love to hear how Thiel using his money to bring about a just outcome does harm to the integrity of the legal system.