No. Somewhere here I debunked the article upon which this is based. The issue was that, unlike Rome, Alexandria and Antioch's ecclesiastical boundaries did not coincide with what had been the civil boundaries. Libya and the Pentapolis, mentioned in the canon, had just been joined to the civil administration in Egypt just a generation before Nicea, having been separated from Alexandria/Egypt for three centuries before that. For Rome, it had ruled the three Western parts of the tetrarchy, hence the Patriarchate of the West.
How the fourth was divided, with the second and third cities of the empire in the same Diocese, needed to be hammered out, a problem not present in the West.
This had been the extent of Alexandria's civil jurisdiction
and, once the dust had settled, the generation (or two) after Nicea:
Things did not change for Old Rome until around this time, with the rise of New Rome. And, contrary to your linked apologist's claims, the Councils and Church did "dare" to tough Old Rome's jurisdiction, turning over all of Moesia Thracia to New Rome.
A better translation can make this clearer:
Let the ancient customs prevail which were in vogue in Egypt and Libya and Pentapolis, to allow the bishop of Alexandria to have authority over all these parts, since this is also the treatment usually accorded to the bishop of Rome. Likewise with reference to Antioch, and in other provinces, let the seniority be preserved to the Churches. In general it is obvious that in the case in which anyone has been made a bishop without the Metropolitan’s approval, the great Council has prescribed that such a person must not be a Bishop. If, however, to the common vote of all, though reasonable and in accordance with an ecclesiastical Canon, two or three men object on account of a private quarrel, let the vote of the majority prevail.http://www.holytrinitymission.org/books/english/councils_ecumenical_rudder.htm#_Toc34001967
You're on the right track. Welcome home!