Den Haag was a key city. Rotterdam is assumed to be included in the Amsterdam province because if split up then Rotterdam would be the important trade node and Amsterdam an important center of trade.
This is why it makes more sense to have Den Haag and Amsterdam (plus Rotterdam) then to have South Holland with assumedly representing both Den Haag and Rotterdam and North Holland having just Amsterdam.
This line of reasoning doesn't make sense to me at all. Rotterdam is located south of Den Haag and is therefore part of the Den Haag province on the map in the original post. I don't see how it can be 'assumed' to be included in another province.
Besides, it is not even true that Rotterdam would be such an important trade node during this period, as it only reached its current status as the main port of the Netherlands long after the EU IV period.