I don't think equating Republic with having representative government really works - there are too many countries which are called Republics which don't have representative government, and other countries which aren't called Republics which do have it.

I mean, you can't really say that countries like Sweden or Holland or Spain or Great Britain, none of them "Republics" don't have governments at least as representative as France or the USA or Argentina.

Essentially a Republic means the ceremonial or actual head of state isn't there because his father had the job. Which normally means the USA qualifies. (Not so sure for the next four years...)