All the court is saying is that if you enable comments on your site you need to at least have some mechanism by which people can get them reviewed and if appropriate removed. As usual this being an EU story it gets blown out of all proportion.
According to the article, it's a bit more than that:
In addition, the website did not appear to take any proactive steps to remove the defamatory and offensive comments, relying instead on automated word-filtering of certain vulgar terms or notification by users.
So a "mechanism by which people can get them reviewed and if appropriate removed" isn't enough, they have to proactively read every comment and remove anything defamatory. However, they may have been able to pass the liability on to the people making the comments, if they hadn't allowed anonymous posting.
So a website in Estonia should either check every comment, I suppose ideally before publishing it, or ensure that they have the true name of every commenter. Perhaps the latter wouldn't be an issue in the US, since true names would be available from the NSA in most cases anway.