The first bit can be news, you're right. Posting the sex video though wasn't, not even a little bit. They could easily have posted the audio of the racist rant. They could have made a super cut of racism and blanked out the sex. They did they opposite though.
Second point, he didn't "run around promoting it" he acted like he was cool with it when questioned about the topic while at the same time assisting the FBI with a blackmail investigation regarding the tape. The blackmail investigation makes up most of the non-public documents looked at during the case.
So, they could have run a news article, but they didn't. They ran part of some blackmail sex tape footage.