I'm less inclined to see this as a copyright infringement. The Mouth Peace tried reposting it with a claim of "safe harbor" because he wouldn't see any profit from the use of the copyrighted material, but that doesn't give people leave to reproduce copyrighted material without permission. The property rights of the owner allow him or her to determine the circumstances of publication, not anyone else. Since the entire songs were used in this publication, it doesn’t qualify under "fair use" excerpting either.
There are two problems with this analysis. First, if I remember correctly the video in question did not reproduce entire songs - extensive portions, but not the whole thing. Second, YouTube is saturated with amateur videos using copyrighted songs in their entirety. We have yet to see the mass yankings of those vids.