Targaryens were obviously a Targaryen noble family, but Valyria has no ruling family. If you believe I am so stupid as to imply a modern democracy, then it's not my problem. Republic doesn't mean there are no noble families, and noble families don't mean that there's no republic. Republic = a system of government without a monarch. Take republican Rome for example - it had a clear cut aristocracy, but no one in their right mind could claim it had a single ruling family. Valyria was a freeholder republic, like Volantis - with elected triarchs (consuls) and, presumably, senate-like body. You pulled the ruling family part out of your ass.