That's, at best, misleading. Voting is a key mechanism by which preferences are aggregated in a democracy, but citizen engagement and participation is the essence of democracy.
> If you believe in democracy, you know your vote makes a difference every time.
No, if you believe in democracy and understand it, you realize your vote very rarely makes any meaningful difference, but that your engagement (including voting) over an extended period of time can.
I don't think so. Talking about engagement and participation is very well, those are indeed important aspects of a citizen's life, but they can also happen in regimes which are not democracies.
Democracy means the sovereignty of the people. This sovereignty is embodied at decision time, which is elections/votes. Most certainly freedom of speech, good education, political debate, etc. are requirements for a democracy to be healthy, but these traits can be found in other regimes.
> you realize your vote very rarely makes any meaningful difference
It all depends on how you define meaningful, I guess.