I think there's a spectrum of democracy from minimal (with peaceful transitions of power, but with other trappings of democracy largely ineffective or absent) to full (exemplifying Ernest Naville's words: "in a democratic government, the right of decision belongs to the majority, but the right of representation belongs to all"). I think full democracy requires minority rights and the rule of law, but maybe that's implied by the Naville quote.

Notably, majority rule isn't sufficient for full democracy, and isn't necessary or sufficient for minimal democracy.