It's not actually inherently democratic because the electoral college often votes against its mandate. In fact one representative of Washington State refused to vote for Hillary even though she won it in this election just gone. So just over 500 people actually have the power to choose the president regardless of who the people actually vote for.
Also the fact that most states vote exclusively for one candidate means that for most Americans their vote simply does not count.
To me democracy is the rule of the majority and the US system is set up in such a way that you can win without the majority supporting you, that isn't a proper democracy.