Power sharing agreements between the powerful who are not accountable to the people isn't something I'd classify as "democratic".
I'd consider term limits to be anti-democratic anyway. A functioning democracy has the ability to boot politicians out, and the people within the democracy, not the law should be trusted to make that decision.
As how the US president is selected by the electoral college. The system used today is a far cry from the original scheme. Look closely and the original doesn't look very democratic, even by the standards of the time. Democracy is an idea, a collection of principals. How it is actually implemented varies considerably.
The Electoral College itself exists as a way to help keep the Executive Branch separated from the Legislative Branch. Congress (aka the Legislative Branch) can step in in place of the Electoral College if the electors deadlock to a point of no recovery, but this is considered highly unusual and an undemocratic act because it violates the Separation of Powers safeguard.
But a better comparison would be the "election" of a Pope. It's only among Cardinals, who tend to vote for a Cardinal to become Pope. Even though a vote is taking place, we are not talking about a democracy.
As to which is closest to an ideal democracy in practice: America, Vatican City, or China, the contest in my mind is who is in second and third place, not first.