The substance of a democracy is the specific mechanism that resolves policy conflicts. ... What does it mean to call for a "democratic" solution if you don't have a conflict-resolution mechanism in mind?

I think that for many people the "substance" of democracy is not the specific mechanism, but rather the general mechanism, and the nature of the output. The mechanism must include at least some formal representation of every member. The details of this don't matter so much: it might be direct voting (strictly equal power), or it might be a representative system (so long as the reps for each voter are more or less equal in power). And the general nature of the output is that it should be fair. Exactly what fair is, is a good question, and probably varies a lot. But at least this: conflicts should not always be resolved in favor of the same person or group or class.

This is not a particularly well-defined notion; clearly it does not resonate with you, who want a stricter definition. But it is hardly a meaningless notion, either. It is not an applause sign.

It is also, I think, a much more useful concept than you seem to have in mind. You are hung up on specifics: "the resolution process can be a direct majority vote, or an elected legislature, or even a voter-sensitive behavior of an AI, but it has to be something." Yes, in any actual project for developing AI, it would have to be something, and something specific. But specifically which of these methods (or an infinity of other specific implementations of "democracy") did not matter to the speaker you refer to.