Does Mage Armor counts as armor in the sense of Monk's Martial Arts or Unarmored Movement requirements? Both features require you to not be wearing armor. (I already know that Mage Armor and Unarmored Defense do not stack but this is a different situation.)
Unarmored movement says
... your speed increases by 10 feet while not wearing armor
Martial Arts says
... you gain the following benifits while you are unarmored ...
Mage Armor says
... a protective magical force surrounds it until the spell ends ... ends if the target dons armor or ...
This spell does not give you armor—it gives you a protective magical force—so it has no effect on these abilities.
Note that it does not stack with unarmored defence—you get whichever is better.