Is Gawker the root of the problem, or a symptom of a larger one? Perhaps the problem is that people will ingest and internalize information from anywhere, without putting it through any sort of critical-thinking funnel. They let themselves become so convinced of something they read on gawker, that they actually try to convince other people it's true.
To put it another way: sure, good riddance to gawker. But what's to stop its successor? You may not like gawker, and your reasons may be valid, rational, or even altruistic. But you cannot dictate the will of its audience. What gives anyone, government or otherwise, the right to stop information at its source?
If you want to lessen the power of information, regardless of how "right" you think it is, the best way to invest your time or money is into teaching people how to think critically, and also why to think critically. Unfortunately it's quite difficult to teach on that subject when you're silencing an opinion from one side of your mouth, and preaching critical thinking from the other.