Fixed. It was originally Amsterdam, but I was experimenting with resolving ambiguous capitals by using the de facto seat of government, based on other feedback here (e.g. South Africa originally had multiple capitals). I've switched back to the more familiar atlas capital in ambiguous cases.
Excellent point. I've removed Vatican City from the map for now, as it is entirely enclosed by another capital city (Rome) and so its Voronoi cell will be tiny.
I suspect this is more of a collaborative scientific effort rather than a commercial enterprise. However, they do mention in a tweet that they are supported with funding from the Flatiron Institute (Simons Foundation):