He’s obviously using “burn it down” figuratively. He’s saying he wants to defeat the climate of toxic, closed-minded PC liberalism that is currently smothering higher education. That is not even close to hate speech. I don’t see anything in the article that constitutes hate speech.
I agree that’s he’s probably using the phrase “burning IT down” figuratively, with “it” referring to the culture of intolerance or some similar idea. But I think the quote was DELIBERATELY edited to suggest that he’s talking about burning down actual buildings.