They are using the term in the generic sense. The government is selected by the people is some form. All those people you are getting outraged at know very well how the government works. They are not wrong to use the term "democracy". Your outrage is misplaced.
“When the people find that they can vote themselves money, that will herald the end of the republic.” ― Benjamin Franklin Or the one often missatributed to Ben “Democracy is two wolves and a sheep voting on what’s for dinner.” I think I’ve seen it with the additional “A Republic is when the sheep is armed.”