So, YouTube has automatic matches for CERTAIN copyrighted material through Content ID. Keep in mind that when a video is identified in content ID, the copyright owner has the option to take the monetization for themselves. So, just because a video is available to watch doesn't mean that the person who uploaded it is getting the ad revenue -- that money may already be going to the copyright owner, in which case, they wouldn't necessarily care about taking down the video.
However, the problem is that not every copyright holder is in Content ID. If a work is not in content ID, then it must be manually identified (either by the copyright holder or by someone in the community), and the copyright owner has to manually submit a takedown notice to take it down
So, when you see videos that clearly include copyrighted materials, there are a few possibilities:
1) it was automatically recognized in Content ID and the copyright owner decided not to block/take down the video
or
2) the work may not be in content ID, and the copyright owner may not be aware that the video is up.