I suppose we can't know the answer to this question, but I think it's worth hearing other people's best guesses. My theory is that Greece is special because it’s mostly comprised of many small islands. Expanding a kingdom from one island to two is much more difficult than expanding a kingdom on land. Each island had its most powerful family and it would have been [more] natural for them to see each other as rough equals. Democracy would have been an obvious government type when the islands needed to make a collective decision.
Each of the Greek city states had its own constitution. Some had kings, others were ruled by an aristocratic oligarchy. Democracy (in the original Greek sense of the term) was basically limited to Athens. It is not true that Greece was “mostly comprised of many small islands”; Athens in any case is not an island. So your linkage of democracy and islands does not really have anything in its favour.
It didn't, that kind of tribal "democracy" isn't special to Greece. Lots of tribes make collective deicisions in a more or less democratic way. Greek democracy excludes most of the population who arent citizens. That's not different from other societies where only the priviledged caste can participate in government. Greece is just remembered specially today because it was the inspiration when real modern democracy was being setup in the last few centuries.