http://www.merriam-webster.com/dictionary/republic
republic
Full Definition of republic from Meriam-Webster's dictionary:
1 a (1) : a government having a chief of state who is not a monarch and who in modern times is usually a president (2) : a political unit (as a nation) having such a form of government b (1) : a government in which supreme power resides in a body of citizens entitled to vote and is exercised by elected officers and representatives responsible to them and governing according to law (2) : a political unit (as a nation) having such a form of government c : a usually specified republican government of a political unit
I’m embarrassed for you that you’d want to debate this with people without having ever opened a book on political philosophy.
Parliamentary systems are also contain facets of democracy but are not true democracies.
Yea, the dictionary definition of a republic allows this country to be called a republic, given a reasonable amount of leeway for the specifics. It’s a democratic republic, but the adjective “democratic” is not the noun which names what this country is: a republic, and Federalist 39 gets further intonthe weeds and calls it a “compound republic”, (which is so right).