"We claim that Dahl’s theory of polyarchy (1971, 1998) provides the most comprehensive and most widely accepted theory of what distinguishes a democracy based on six (1998,p. 85—originally p. 8 in his 1971 book) institutional guarantees (elected officials, free and fair elections, freedom of expression, alternative sources of information, associational autonomy, and inclusive citizenship). This conception requires not only free and fair elections but also the freedoms that make them meaningful, and thus avoids the electoral fallacy (Diamond, 2002; Karl, 1986). "
> 'When I use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean — neither more nor less.'
> 'The question is,' said Alice, 'whether you can make words mean so many different things.'
Whatever caveats need to be added or however much it would differ from our ideal, I've never seen anyone call the form of government of Athens in the period between the Persian War and the Peloponnesian War anything other than "democracy." The Roman Republic, for whatever it's short comings, was a republic. America in 1790 or 1850 was at least as democratic as either of them (by the six measures you list, or by any other useful measure).
Even moderate political scientists rank the US below the democracy line. And calling Australia a liberal democracy is also a stretch.
Independence of the 3 government powers plus press and education would be needed for a modern democracy.
Looks like a CIA puff piece.