Isn't this some extreme distortion of semantics though? Going by the majority usage of those words, "democracy" and "republic" mean different but not incompatible things and the claim that America isn't a country is just baffling.
Yeah, republic doesn't really mean much these days (in the common definition and applied to contemporary countries).
North Korea is officially a republic, but it's closer to a hereditary, absolutist monarchy in practice. The UK is officially a constitutional monarchy, but in practice not all that much would change, if they demoted the royal family.