In any event "retribution" is an overly simplistic way of looking at what Thiel did. It could also be interpreted as protecting future victims of Gawker.
Suppose someone stabs me, and I live. For whatever reason, they get away and continue to run around stabbing people. If at some point in the future, they attempt to stab someone else and I stop them, killing them in the process, is that killing in retribution or protection? Maybe both. It doesn't really matter so long as we can stop people from getting stabbed.
Gawker went and made a powerful enemy for no good reason. Outing someone who didn't want to be outed helped no one. Thiel used the considerable means at his disposal to ruin Gawker in a way that didn't harm anyone other than the owners of Gawker. Since nobody else really benefited from Gawker's existence it's unsurprising that nobody else really cares if they stop existing.
If Gawker had been exposing powerful people doing something illegal or otherwise harmful instead of just being gay or having affairs, they would have had the justice system and the public on their side and they wouldn't have lost the lawsuit.
"Moral obligations" are made-up. Obligated by whom? What happens if someone doesn't fulfill their moral obligation? Nothing, right? Maybe someone writes a comment on the Internet saying they should be ashamed, but that's pretty much it.
Feel free to pontificate all you like about the morality of it. That won't change the fact that it did happen and will happen again unless a force powerful enough to stop it chooses to do so.
Ultimately, the whole point of having a justice system is to sort out these questions. Anybody can sue anyone else for any reason. We depend on the courts to sort out the ones that are valid from the ones that are invalid. In this case, the courts deemed this a valid lawsuit. If you disagree with the validity of it or feel the methods by which the courts make these judgments is flawed, then that's one thing, but the rules of the system allow any lawsuit to be brought for any reason.