That trivial definition sees limited use in the real world. Few countries that are popularly considered democratic have direct democracy. Most weigh votes geographically or use some sort of representative model.

Most established definitions of democracy goes something like, heavily simplified:

1. Free media

2. Independent judicial system

3. Peaceful system for the transfer of power

The most popular model for implementing (3) is free and open elections, which has yielded pretty good results in the past century where it has been practiced.

Considering social media pretty much is media for most, it is a heavily concentrated power, and if there can any suspicions of being in cahoots with established political power and thus non-free, surely that is a threat to democracy almost by definition.

Let's be real here: It has been conclusively shown again and again that social media does influence elections. That much should be obvious without too much in the way of academic rigor.

Of course social media influences elections. Direct or indirect, the principle of democracy is the same: the electorate hears a diversity of perspectives and votes according to the ones found most convincing.

How can you say you believe in democracy when you want to control what people hear so they don't vote the wrong way? In a democracy there is no such thing as voting the wrong way.

Who are you to decide which perspectives get heard? You can object to algorithmic feed ranking only because it might make people vote wrong --- but as we established, the concept of "voting wrong" in a legitimate democracy doesn't even type check. In a legitimate democracy, it's the voting that decides what's right and wrong!

You write as though the selection of information by algorithmic feeds is a politically neutral act, which comes about by free actions of the people. But this is demonstrably not the case. Selecting hard for misinformation which enrages (because it increases engagement) means that social media are pushing populations further and further to the right. And this serves the interest of the literal handful of billionaires who control those sites. This is the unhealthy concentration of power the OP writes about, and it is a threat to democracy as we've known it.

By that logic, the New York Times also threatens democracy. Of course, it doesn't, and that's because no amount of opinion, injected in whatever manner and however biased, can override the role of free individuals in evaluating everything they've heard and voting their conscience.

You don't get to decide a priori certain electoral outcomes are bad and work backwards to banning information flows to preclude those outcomes.

No. The difference is that the New York Times has not been specifically engineered to be an addictive black hole for attention. Algorithmic social media is something new. Concentration of press power has always been a concern in democracy and many countries have sorted to regulate disability of individuals to wield that power. We get to choose as a society the rules on which we engaged with one another. Algorithmic social media is an abuse of basic human cognitive processing and we could if we wanted agreed that it’s not allowed in the public. It’s not a question of censoring particular information or viewpoints. – Here is that the mechanism of distribution itself is unhealthy.