What do you mean GG'd? The government would say, "You have this piracy crap on your site, take it off or else. You have 5 days." Then you would delete the stuff from your page.
The law doesn't crack down on just any random site owner, just those who refuse to do anything about piracy. Badspot has a zero-tolerance policy for piracy, and he has almost zero problems with it. I think if every site owner had the same views, we wouldn't have a problem.
They don't GG them because the site does something about it. You're absolutely right. I'm not talking about the direct effects of the bill, I mean the means by which the site will need to approach avoiding violation of the new legislation. Right now, YouTube has to aggressively mute and remove videos because they have to avoid lawsuits because of copyright infringement, and the offer the means to appeal if the user is willing to take legal action. Similar policies would have to be made, perhaps even more aggressively depending, to avoid action by the government, and the appeal process for that would be a bit out of YouTube's hands.
The bill may not make the website owner automatically receive punishment, but it would mean that they would have to be much more careful about making sure no content is uploaded to their site, or no content remains on the site, that might cause an offense on their part. Again, the website is essentially punished ('punished' used more loosely since it's not direct) for 'having the means of piracy', and this is passed onto the users of that site.