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?
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.