Republic back then meant commonwealth with any form of government. The Dutch Republic was loose union of seven provinces. Republic changed to mean democratic government by representatives without monarch.
The US itself didn't start off very democratic, and could have stablized into a more oligarchic nation if it kept the notion of only allowing property owners to vote. Originally, land ownership wasn't a high barrier of entry, but in a more modern era corporations or oligarchs could own most of the land, and lease it out to prevent anyone else from gaining a vote.