I wanted to disagree with you and say that is simply not a hereditary monarchy, but after a moment I think you are right.
Monarchy connotes the existence of some sort of elite class and even in cases the monarch was elected it was always from the aristocracy, founding families, or royal family.
The idea that a leader chosen randomly from the general population is a monarch feels like it would muddy the meaning of monarchy to the point of uselessness.
That is, by definition, not a monarchy