He's simply financing a non-spurious lawsuit, which the courts have decided was legitimate. This is exactly what I want the billionaires in our society doing.
He may be acting in his own self-interest, but it also happened to align with the public interest. And if the courts had decided against Hogan, it all would have been for nothing. There is no grand problem here. He isn't "destroying publications he wishes to silence", he's augmenting the resources of someone with a legitimate legal claim against the newspaper.
If you are putting forth the argument that merely financing a lawsuit is a corruption of the public trust, then we have much more serious problems with our legal system than Peter Thiel having it out for Gawker. Anyone should be able to fund any lawsuit that they want, and then the courts will decide if that lawsuit has merit. That's why we have courts in the first place.