It's a counter-revolution because the communists won the last election and the Roman curia and the landowners didn't like that.
My friend is playing Victoria 3 with the goal of taking the Papal States to an Anarchist Theocracy. The current step of the process is instituting a Council Republic which is having some historically-familiar issues. As I was writing this, though, the counter-revolution failed. All hail Pontifex Populi Pasquale Airenti! Onward to the An-Cath future!
you can't see from this screenshot but this is indeed an anarchist distribution of power, except for Pope Girolamo who is in charge