Neither does the Rome of today.
That does not change the fact that John was referring to Rome at the time it was written.
According to the Unam Sanctum and the "two swords" doctrine, Rome, or rather the Vatican does rule both the ecclesial and secular or "temporal" world as denoted in the following declaration from the "Unam Sanctum":
We are informed by the texts of the gospels that in this Church and in its power are two swords; namely, the spiritual and the temporal. For when the Apostles say: 'Behold, here are two swords' [Lk 22:38] that is to say, in the Church, since the Apostles were speaking, the Lord did not reply that there were too many, but sufficient. Certainly the one who denies that the temporal sword is in the power of Peter has not listened well to the word of the Lord commanding: 'Put up thy sword into thy scabbard' [Mt 26:52]. Both, therefore, are in the power of the Church, that is to say, the spiritual and the material sword, but the former is to be administered _for_ the Church but the latter by the Church; the former in the hands of the priest; the latter by the hands of kings and soldiers, but at the will and sufferance of the priest.
However, one sword ought to be subordinated to the other and temporal authority, subjected to spiritual power. For since the Apostle said: 'There is no power except from God and the things that are, are ordained of God' [Rom 13:1-2], but they would not be ordained if one sword were not subordinated to the other and if the inferior one, as it were, were not led upwards by the other.
It has been a long standing doctrine of Rome that the Roman church and pope of Rome are the supreme rulers of both the ecclesiastical realm as well as the temporal realm.
If that's the case, your bone to pick is with Christ Himself for "foolishly" giving Peter the, um, KEYS to the kingdom of Heaven. If it's an either/or with you, then you need to hang your hat on the words of Paul or the words of Christ, take your pick. If you believe that Scripture cannot contradict itself, then there has to be a relationship between Paul's words and Christ's words which demonstrate correctness in both statements. That's the problem with relying on a black-and-white approach to the Gospel. You read it like it came off an IBM supercomputer, and not imbued with a specific intent of a human author inspired by the Holy Spirit.
>> It has been a long standing doctrine of Rome that the Roman church and pope of Rome are the supreme rulers of both the ecclesiastical realm as well as the temporal realm. <<
Doctrine is eternal. Eternal is antonymical to temporal. Hence, doctrine can never describe the temporal. The Vatican was once supreme ruler of the temporal realm of much of Europe. It is not today.