You’re right about the nature of the phenomenon, but it didn’t begin on the internet. It comes from writers who taught at expensive private schools in the ’70s and ’80s: Derrick Bell, Kimberle Crenshaw, bell hooks, etc. A black socialist critic of the phenomenon, Adolph Reed Jr., calls their ideology identitarianism for the obvious reason: they reduce everything to social identity.
They claim to believe in “intersectionality”, which might make you think they’re concerned with the ways different factors play off each other, but you would be wrong. Under their form of intersectionality, all forms of oppression are disconnected and only intersect, so if someone is talking about race or gender and a listener tries to discuss the ways class affects those issues, the listener will be accused of “derailing” the discussion. Because identitarians are evangelical, they want to keep everyone on their rails.
The evangelical naure comes from “social justice”, a concept that began with Italian Catholics in the 1840s and spread to other religions. It’s only been adopted by some atheists in the last couple of decades—if you search the speeches of the civil rights era, you’ll find few if any references to social justice. Martin Luther King was far more interested in economic justice.
I don’t think of identitarianism as the New Leftism because many of its supporters are neoliberals, conservative Democrats who prefer Hillary Clinton to Bernie Sanders. I think of it as New McCarthyism, because it’s driven by privileged people who want to control what the rest of us may say.