You are talking about direct democracy, which is but one kind of democracy. Representative democracy is still democracy.
Remember that Plato defined democracy in opposition to monarchy and aristocracy. Universal suffrage, freedom to form parties and to manifest against the government are (part of) what defines modern democracies. Even Switzerland only resorts to referendums in relatively rare cases.
Remember that Plato defined democracy in opposition to monarchy and aristocracy. Universal suffrage, freedom to form parties and to manifest against the government are (part of) what defines modern democracies. Even Switzerland only resorts to referendums in relatively rare cases.