It's a democracy in terms of the electoral process, mostly... at least historically. Flawed, but the people select their leaders by election.
It's not really a democracy in terms of political culture and rights. Very weak free speech, right to organize, right to assemble, freedom of the press, etc. They jail a lot of journalists, on charges like "subliminal messages announcing the military coup."
However, it all comes down to this, what happens when people of a democratic country elect a president that has totalitarian tendencies?
Japan's Abe is famous for auctioning huge reserves of JPY in order to reduce the value of their currency and stock up on USD. Reduced currency value means their exports became temporarily cheaper and this way they got an artificial boost to their production industry.
This is a complex subject and doesn't show that "country X is the puppet of country Y", it rather shows how they like to strategize for their own benefit.
[edit] Can't reply below: Freedom House is NOT the State Department. They're a funder, but not the only one. So your description still in incorrect or requires sourcing.
They're not masquerading in the sense that they try to hide where the money comes from, but to the majority that read their materials, this won't be apparent.
If they are a government organization then the domain needs to be .gov.
.org gives the perception of NGO.