As I understood it, the law applies to all search engines located in the EU (so they could easily just leave the EU and the law wouldn't apply), it's just that Google is being focussed on because it's the most popular.
The book proposal Gawker published consists of lots of details and snippets of her forthcoming book. I don't think Gawker can justify posting the full proposal as fair use, since the original post consisted primarily of insulting comments aimed at Dunham and her polarizing personality, rather than of the proposal and proposed book.
Given she has to sell way more than $3.7m worth of books, can you really blame her for attempting to pull 66 pages worth of proposed contents and samples of said contents? Also, this just gives her way more publicity and think she knows (and probably doesn't care) just how love/hate she is...
I think they're on about illegal live streams, not youtube videos (eg. A load of illegal BBC Sports streams popped up during the world cup, which is odd because we can watch it live on the iPlayer anyway)