Actual political scientists 100% for sure do not split hairs like that unless there's a reason they're trying to distinguish between two flavors of democracy and there's risk of confusion, and would definitely describe any part of the American election system as falling under the umbrella of "democratic". For one thing, it's not some kind of club with very strict rules for inclusion and being in or out is super important in some kind of way, and for another it would mean almost no systems or parts of systems would be "democratic" so we'd just have to invent another word to take over the very useful role that word serves now.
[EDIT] to be clear it's fine to think some parts of our election systems suck (they definitely fucking do) but "it's not democratic" isn't a very useful, meaningful, or even clear objection, per se.
[EDIT] to be clear it's fine to think some parts of our election systems suck (they definitely fucking do) but "it's not democratic" isn't a very useful, meaningful, or even clear objection, per se.