I bet it would help less than you think. Because a lot of people who pirate wouldn't buy the game any way. And, unlike physical goods, if you download something you would never have paid for, you're not taking sales away from the producers.
Still, the owners of the site said they complied with DMCA and copyright claims, and pulled those files. But there's no way they could possibly check every single file for copyright infringement. Firstly, how would you know that MyGraduation.avi was actually a pirated copy of The Dark Knight? Secondly, what if the file is under copyright, but the content creator used the Creative Commons license that allows for free distribution and use of the content? Is the site supposed to contact every creator and double check that?
A lot of time, effort, and money would be saved if the big media corporations just realized that consumer demand has changed and aren't satisfied with the old distribution models. We want streaming and downloadable content, on demand. And we're willing to pay for it, or watch advertisements (like on tv). Bootleg recording of live Dave Matthews Band concerts used to run rampant. Then the band starting recording their concerts and selling them. The bootleg market dried up, and the band made a ton of extra money.