Didn't Mesopotamia cover most of what is now Iraq, as well as the Kingdom of Babylon. And wasn't today's Iran known as Persia. And what about Israel (Judah, Judea). Certainly these are older than many of those targeted in the quiz.
You can check out my source for more info, but I believe Mesopotamia and Judah never had formal declarations of sovereignty that were recognized on the world stage until later. Also remember that both countries were part of the British empire at one point. As for east Asia, I believe this region was more developed in early years and had an international community that recognized other states as independent. Overall, I believe the only truly accurate countries on this list are several of the European countries, along with Oceania and the Americas. This is because the best records are kept of these regions due to European colonialism.