Politics

No, that is a misrepresentation of the source you provided. Back in the time when (early) modern political science was invented, republic was indeed a catch-all term which did mean that some kind of representative government was involved, because the role of head of state was not heritable, ie. it was not a monarchy. So the role of head of state must necessarily be through some form of representation, usually election (although the group of electors was mostly not very representative of the general populace).

That is why in the 17th and 18th centuries republic was used as a slogan of opposition to monarchy (and oppression in general). Because having a system where the role of head of state wasn't heritable was the opposite of what was the majority type of political system at the time, regardless of what the rest of the political system of that country was.

But throughout the 19th century and especially 20th century, monarchies lost their majority position, and a host of other political systems appeared. Not least the appearance of representative democracies in the Western world.

At that point republic does symbolically still mean some kind of representation, the republics of Saddam's Iraq, or China, or even North Korea, still involves voting, even though they are dictatorships in practice. On the other hand several Western democracies are not republics, but constituional monarchies. That is because the juxtaposition of republic/monarchy is virtually meaningless for most countries now, it defines nothing at all about the actual political system of the country.

The US is indeed a republic, because the role of head of state isn't heritable. But that is all that the term means in connection to the American constitution. Back in the 18th century republic was the term they used, because of the aformentioned reasons, most of the founding fathers did not set out to create a democracy, and the radical democratic faction was also pushed aside when it came to writing a constitution. However through the following centuries, the American political system was slowly changed towards democratic institutions, lastly in 1964 with the Civil Rights act which finally introduced universal suffrage. Of course a lot of the democratic development has since been undermined again, especially this last decade, and of course mostly this last year.

But in modern political scientific terms, the US is a republic and a representative democracy still (even though the constitution is meaningless with the current govermnent), and the most defining part of it is the representative democracy part.

Also you seem to have missed this part in the link you provided:

Despite its democratic implications, the term was claimed in the 20th century by states whose leadership enjoyed more power than most traditional monarchs, including military dictatorships such as the Republic of Chile under Augusto Pinochet and totalitarian regimes such as the Democratic People’s Republic of Korea.