The question is a bit too broad to be answered for real, but i'll give a small attempt.
Democracy is the only known stable equilibrum in politics - or as close to it as we can get, due to the fact that:
"Developed" country is defined on Wikipedia as:
A developed country or "more developed country" (MDC), is a sovereign state that has a highly developed economy and advanced technological infrastructure relative to other less developed nations. Most commonly the criteria for evaluating the degree of economic development is gross domestic product (GDP), the per capita income, level of industrialization, amount of widespread infrastructure and general standard of living
Due to the nature of democracy, when the environment changes, you have a chance to adapt to, either from the top (by electing people who aren't as wrongheaded) OR from the bottom (by simply doing things because you have the power - witness Internet economy.
In any other form of government, you either have to hope the dudes at the top (who for most of human history obeyed the Peter Principle, and even the good/smart ones are usually not smart enough for complex modern systems of today's economy/technology) get things right, OR, have a violent regime change to get rid of the ones who don't get things right. The former rarely happens; the latter isn't very conductive to economy, infrastructure OR general standards of living.