This sounds close to Russell's "class of all classes" paradox. Is it?
Yes the type theoretic analog to Russel's (set theoretic) paradox is Girard's (as mentioned in the abstract) paradox.
It is Burali-Forti 1897, predating Russel's paradox.
Yes the type theoretic analog to Russel's (set theoretic) paradox is Girard's (as mentioned in the abstract) paradox.