Democracy (Miriam-Webster):
1 a: government by the people; especially : rule of the majority b: a government in which the supreme power is vested in the people and exercised by them directly or indirectly through a system of representation usually involving periodically held free elections
Let's be very, very clear here. The rule of the majority is a big part of "democracy" but it is not synonymous. And I'm going to detail why majoritarian rule is a stupid idea, and what distinguishes liberal democracy, and particularly our federal democracy, from majoritarian rule.
The Senate is nonmajoritarian. Majority-minority congressional districts are nonmajoritarian. The requirement that supermajorities of states are necessary to change the constitution is nonmajoritarian. And the primary conventions are nonmajoritarian.
This does not mean they are undemocratic.
The popular vote argument is probably the least persuasive metric I can think of, and was as unpersuasive in 2000 as well. Democracy is not solely about who, or what issue stance, gets the most votes - although that's quite an important part of it. It's also about creating stable institutions that guarantee that basic civil liberties and minority rights are not governed solely by the whim of an easily persuaded public.
The very founding of our country, as flawed as it may have been, enshrined nonmajoritarian rule in the upper house of the Senate. Why would Rhode Island get to be as powerful as New York? Because in a nonmajoritarian, but nonetheless democratic system, we have certain guarantees for the representation of small states. This may lead to somewhat perverse outcomes (read, farm subsidies), but what is important is that the basic institutions of our country - including the electoral college as derived from the Senate - disproportionately weights small states precisely to protect their voice in our democracy. This is reflected in the Democratic party's nomination process, and rightly so.
Why should we gerrymander districts to ensure majority-minority status? This is highly questionable from a democratic standpoint, particularly when geographic contrivances must be stretched to the limit in order to accommodate this subversion of majoritarian rule. We do it because in a just democracy we guarantee that minority voices are granted access and voice to the institutions of government. This is reflected in the Democratic party's nomination process due to their allocation of pledged delegates by congressional district, allowing minority candidates with an overpowering win in certain districts to garner additional votes, and rightly so.
Finally, why do we require such rigor, including the consent of 3/4 of the states to change the constitution? Because our democracy is federal, guaranteeing large rights to even the smallest of states to guarantee their freedom to set social and economic policy without interference from the federal government. While the genesis of this idea was likely slavery, it remains important today, as the ruling of California's Supreme Court guaranteeing the right of gays and lesbians to marry in that state without Federal interference shows. This is reflected in the addition of DNC superdelegates to the Democratic party's nomination process, disproportionately numbered in favor of the small states, and rightly so.
In summary, the popular vote, or measures derived from there (i.e. votes per pledged delegate) reject the basic Federalist, minority-rights guaranteeing premise of our peculiar American democracy. The rules are there not to thwart the will of the majority of the people - but rather to tweak it in such a way to guarantee that our small states and our minorities will be heard. And rules to guarantee such things are not only compatible with democracy, but I argue, requisite for it.
It's all well and good if you want to argue that such a system is not fair, or not right from your perspective. That's your prerogative. But it's certainly not undemocratic.