Many countries include 'Democratic' or 'People's' in their names, even though they are not democratic and do not serve their people. Examples:
Democratic People's Republic of Korea
Lao People's Democratic Republic
People's Democratic Republic of Algeria
Democratic Republic of the Congo
And German Democratic Republic (East Side) in 1949–1990.
None of these states are democratic, power and wealth are concentrated in the hands of a small ruling elite. Who are they fooling with these names?
I mean it in Gramsci's terms. For the second question I would say the ones cited by OP are good examples but horizontal organization is my preferred one, look about EZLN ways of horizontal democracy. Again not saying they are the correct or morally good ones either.