In DnD if you have multiple ways to calculate your armor you could only choose one way of doing it. In this case Mage Armor and Unarmored Defence are mutually exclusive.
This is the answer. It has nothing to do with if mage armor is armor or protective aura.
Some spells and class features give you a different way to calculate your AC. If you have multiple features that give you different ways to calculate your AC, you choose which one to use.
