Here's some more of the story:
https://www.thefire.org/yale-students-demand-resignations-from-faculty-members-over-halloween-email/
Yale's Intercultural Affairs Committee sent
this email saying that people should be cautious when selecting their Halloween Costume. Though officially it's just a suggestion, it's sent to everyone and signed by what I assume are some important people, including the Dean of the College Office/Office of Student Life.
Wife of the guy in the video is "Associate Master" and he is "Master". She sends out
this email urging students to think for themselves and have squabbles among themselves about the appropriateness of individual costumes rather than relying on administration to think for them.
Students get mad and organize to meet with a Dean,
described here. "Master" Nicholas Christakis comes out to talk to them too, and that video is part of the result. A bunch of other videos are
in this playlist. They demanded an apology for his and his wife's views against administrative control over free speech, and he didn't give it to them.
Edit: other users have been describing the Halloween emails as "the straw that broke the camel's back" of campus racial tensions. Most recently a party
allegedly turned away black women.
Here's an opinion piece that attempts to summarize.