Incorrect back-formation of Portuguese plural reis. The correct singular is real.
From
Wiktionary
Rei Sentence Examples
The dictator appointed to meet the dangers of war, sedition or crime was technically described as " the administrative dictator (rei gerundae causa).
The only complete translation is Il Libro dei Rei, by I.
Thus in the 5th century, among the comites attached to the emperor's establishment, we find, e.g., the comes sacrarum largitionum and the comes rei privatae; while others, forming the council, were styled comites consistorii.