The commemoration of the anniversary of the diocesan cathedral is a solemnity for that diocese. In the U.S. we don’t do a very good job of celebrating it, outside the cathedral itself, but it’s a solemnity nevertheless.
The Archbasilica of St John the Baptist (the Lateran) is the proper cathedral of the See of Rome, and is thereby the cathedral for the entire Catholic Church. In a way, we could say that all Catholics are parishioners of St John cathedral!
That’s why it is a universal solemnity, because it’s the universal cathedral.