There is such a thing as political/democratic legitimacy, and when you lack it, then people stop accepting you as their president/leader/prime minister. 45 lacks that legitimacy, hence many people do not recognize him as their president. This is a very legitimate sentiment and can present itself regardless of the process through which a leader comes to power: democratically elected, semi-democratically elected, or through means of coercion, coups, treason, etc. It really doesn't matter how one loses that legitimacy, when lost, it's lost.
Now from day one 45 didn't have much legitimacy to begin with, through his lack of leadership and terrible actions he has lost even more of it by now.