Roman Emperors and the \"King\" title

[Robert Vermaat]

If no one else can think of any other instances of “Rex” being used, he must really have been unique.

In fact, there are quite a number of sources from the 4th c. onwards that use the word 'rex' for an emperor. Best read this article:
Fanning, S. (1992): Emperors and empires in fifth-century Gaul, in: Drinkwater, J.F. and Hugh Elton eds.: Fifth-century Gaul: a Crisis of Identity?, (Cambridge), pp. 288-97.

Fanning comes up with a good number of authors having no problem using the title rex for Emperors, including Tertullian, Orosius, Sulpicius Severus, Ammianus Marcellinus, Claudius Claudianus, St. Augustine, Jordanes, Hilary of Poitiers, Prosper of Acquitaine, Venantius Fortunatus, Ennodius, Isidore of Seville, Paul the Deacon, etc.