i don't think youtube is even the target of this; it says "streaming" -- youtube isn't streaming. i mean, it "streams" stuff to your computer in a sense, but my impression is that this is meant more for things like livestream, where people use it to livestream events that you'd have to pay to see otherwise (for instance, blizzcon, or sc2 tournaments)
Pretty sure it isn't. Youtube is a streaming website and this targets people uploading copyrighted material to these sites. I strongly doubt people watching live streams that you'd have to pay for for free is a huge problem for companies, or at least not to the extent that lobbyists would push a new law specifically to prevent it.
Every website that lets you watch videos/listen to music without having to download it first (well except in your browser's cache) is colloquially referred to as a "streaming" website.