"democratic" and "elected" are entirely different adjectives.

The system for electing the US President is very much not democratic, and still the President is very much elected. (Though its less undemocratic than it used to be, when the electors themselves were not generally directly elected by the voters.)

There are indirect elections that are reasonably demoocratic despite being indirect (the PM in some, but not all, parliamentary systems), there are elections that aren't based on anything like a general citizenry at all—e.g., Papal elections. For a leader to be elected is certainly not a sufficient condition for their position to be held democratically (it may be a necessary condition, though.)