You can phrase it that way. But it's a deceptive statement. For the most part, people don't switch parties they vote for. They just choose not to vote instead. So taken in aggregate, you could say "we disliked Hillary so we voted for someone worse".

But the more accurate statement is that some groups of people decided not to vote at all because they disliked Hillary, and other groups of people decided to show up and vote.

The American voters’ approach to government often reduces to “cutting off the nose to spite the face.”

You’re right with regard to your first point: we don’t have directly democratic elections; We have representative (indirect) elections (a la the Electoral College).

With regards to your other point: Hillary did not win the election, no matter how you spin it. She won the popular vote, but that means nothing in terms of who becomes President (read: who wins).

We also don’t “value some people’s votes more than others.” The Electoral College votes based on the way that state’s populace votes, and every electorate’s vote is equal. However, each state can have their own rules regarding how those votes are distributed: some states are winner-takes-all at the state level, while Maine and Nebraska are winner-take-all at the district level.

One can argue whether the Electoral College should exist at all, but it’s worth keeping in mind why it was created: we are a union of states (United States of America), not a homogenous unit (United America?).

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.