YouTube is located in California and is subject to all state and federal laws. Even though they may be serving internationally, the content is still on their servers, and they must remove it upon request.
It makes it an automatic felony to post copyright material, regardless of what the copyright owner actually wants to do. For example, I could upload a video of a game and the copyright owner not care. Without this bill, it's up to the the copyright owner if or when to create a cease-and-desist. With this legislation, it's automatically a felony.