Yes, this image clearly shows that Jews run the whole world.
Kinda strange that the map-maker forgot about us Jews for about 4000 years there, but I understand that it's hard to figure out where to spread around that purple.
In truth, the purple should have been spread back and forth to several places, for instance, in Poland--where three million Jews once lived--but it would always be in a mixture of some other more predominant religious society.
I guess if what the map was trying to say is: "Which countries have Jewish/Christian/Muslim establishments", then yes, I guess there really haven't been any Jewish majority countries in world history but a few.
There was a small empire in Middle Asia I've heard of where Judaism was the State religion, but that was brief, and I'm not sure it was a majority of the people who converted.