Yeah, that pretty much sums it up. Our nation consists of 50 independently governed states, each with its own president, its own congress, its own constitution, its own military, its own police force, and its own laws. The states get to elect the president, not the individual citizens. If we elected the president by popular vote, most of the states in the union would have no say in the matter whatsoever.
Progressives, of course, don't like the idea of a union of states. They prefer a centralized federal government that runs everything from top to bottom. So, they naturally prefer a system in which the citizens elect the president by popular vote. But as you pointed out, we live in a constitutional republic, not a democracy.