This isn't censorship in the "block it because it's offensive" way; it's corporate censorship. If someone were to simply post a picture of something copyrighted, like, say, Mickey Mouse, Disney could demand that the whole site be shut down for "piracy". It's a disgusting law written by corporation and debated by people who don't know how the internet works.
The problem with your example, though, is that if the NY Post started printing your book, it'd pretty obviously have been a decision by the corporate power structure itself, not just some rogue poster. I can understand wanting to protect intellectual property rights, and I can understand why TV companies and record labels would want to take unauthorized things down (though I think their reasoning is wrong). However, if a clip of The Daily Show is posted on YouTube, YouTube weren't the ones to decide to post it; a user did.