If so, is Japan the only kingdom/empire in human history where the rulers have all been from one single family for over a thousand years?
Which emperor are you referring to when you say the first one? There are a number of them (at least the first ten) that are considered to be legendary; although the Kojiki and Nihon shoki (Japan's earliest chronicles) note a number of emperors, they mix fact with fiction and aren't reliable as historical records.
Source: Joseph Kitagawa, On Understanding Japanese Religion