"Wealthy, advanced economies" is quite extensible concept. There are some small, not so wealthy countries on the list. No real correlation here.
And if you are wondering, why Nigeria is not on the list — well, isn't it obvious? I mean, even if the country was very successful during its history, but barely keeping on the float right now — probably the 1000 y.o. family business wouldn't be currently active as well.
Latvia and Slovakia entered after Poland, for instance. Won't check the rest.
And, anyways, does OECD membership really account for something? Who is not a OECD member nowdays? African countries? Well, I believe it isn't a surprise for you there aren't many known thousand-year-old businesses there (there hardly is a "thousand-year-old history" at all, same as South America), and this is not entirely related to a country doing well right now. I bet you don't consider Latvia currently doing better than Arab Emirates, for example.
Basically, most of these old businesses are either in Europe or Japan. I'm only surprised that China, SK and Russia are not on the list, but you can find explanations for that. And whats left are, basically, "countries w/o history".
So, no, I don't believe you could find a causal relationship here, unless you are basically making it up.
And if you are wondering, why Nigeria is not on the list — well, isn't it obvious? I mean, even if the country was very successful during its history, but barely keeping on the float right now — probably the 1000 y.o. family business wouldn't be currently active as well.