Republic is about how the vertex of government is structured.
Democracy is about where the executive/legislative power comes from.
The US is both, you could argue that Canada is not a republic as they have a recognized queen, but it would be a stretch as she has essentially zero power there.
The electoral college is an abstraction so that the states in the United States are able to have a check and balance on federal power. Having a direct democracy of 300 million people would be a bad idea, a lot of political philosophy has been written on why.
If you build on a library that builds on library using AGPL license, you are still bound by the AGPL license, no matter how abstracted. If your country ultimately derives for the people, you are democratic. It is just that the USA is technically a democratic Republic, and intentionally so.
Now I am by no means a fan of the electoral system and I think one van argue that the US fails to live up to being democratic in practice for several reasons (I consider the electoral college a very minot part of the issues), however saying that it can not be democratic by principle or definition it can not be a democracy. I mean let's remember that in Athens (where the term comes from) only a minority of male citizens was allowed to vote.
Unfortunately, that kind of rebalancing has zero political support. The National Popular Vote Interstate Compact, while not as good a solution in my opinion as it doesn't fix the underlying problems with citizen representation, is probably more politically feasible in terms of fixing presidential elections.
Currently it is perfectly possible to win the entire EC minus 2-3 states with less than 50% of the popular vote.
Actually in the US the election of the president is remarkably linear.
In Italy the actual head of state is elected by the parliament (with no underlying direct vote) and then during national elections 1) the people elect a new parliament (with a complex mixture of proportional/non-proportial seats) 2) the parliament proposes various governments to the head of state 3) the head of state selects (and makes suggestions for modifications) the government (the actual executive branch).
And surely there are democracies that follow a more complex process.
The main difference between the US and most other countries is that the US counts votes for the president federally and not nationally, and the difference would almost completely disappear if more states would follow Maine and Nebraska example and drop the Firts Past the Post election style.
Democracy means that the legitimacy of the state is given by the people, not blood, not military, not religion, not oligarchs.
Rather than a boolean, democratic is better understood as a numeric value.
"How democratic are you?" not "are you democratic?"
Dictatorships do exist.
Sometimes power is held by a small group of individuals that control the military and can make dissenting voices disappear.
Sometimes there are elections but the ruling class can simply throw out unwanted votes with impunity.
In both cases power is derived form people, but not The People.
My question for you would be, do you know of a country that IS a democracy by your definition?
There's an old game, Anachronox, that does a wonderful job of making fun of this when the player is on the planet Democratus. Worth a play if you haven't.
When one group is actively trying to absolve its sins of the past, and the other doesn’t even recognize them while doubling-down, the claim that “everyone has sins” an abdication of the idea that behavior matters.