I don't think the grad students the author references are unaware of what humor is or can be, I think they're just aware that the stakes of humor have gotten too high these days.
There's a large subset of people who have decided that all forms of "punching down", when targeted at historically oppressed groups of people, are forms of humor that perpetuate oppression. They aren't entirely wrong, and it's probably good that our generation has lost the excuse that "it was only a joke." It's probably been taken a little bit too far though that any such joke brands you a big-R "Racist" who is just as bad as Donald Trump. So, the risk of ending up in a foaming, angry Tumblr post that goes viral is what's scaring people away from "punching down" at oppressed groups (or maybe sometimes a thing called tact?), which is not an inability to understand humor so much as an inability to speak about it.
I guess it just seems like the author made a relevant observation about our inability to make certain forms of humor and then completely missed the point as to why or which forms of humor are forbidden. It turns out that "punching down" is still pretty easy and common, so long as you don't target specific groups of people for specific reasons. The subset of people who get so offended, the "social justice warriors", are pretty "punch down at" themselves, so long as you don't make assumptions about their gender or sexuality or race or whatever. You can find a whole host of subreddits dedicated to making fun of delusion people who get too enthusiastic about social justice, or have an unnecessarily high opinion of their toughness or intelligence, or whatever. They are all usually a lot more mean than funny, though.
It's probably worth examining what we've lost with our inability to punch down at certain groups, but this article doesn't really go there, it kinda just touches on briefly before making a left turn to Trump.