You are correct that those are the 5 game species that can be "hunted." It is just how they want to call it. Because besides the game species, that have a hunting season.I thought they only hunt 3 bird species and rabbit and hare in Netherlands?
There a also species that can be " managed" during different seasons by those who manage them. Those species are fallow deer, mouflon, roe deer, Red deer and in certain areas wild boar. I for example help managing the roe deer population. The only one of the "manage" species in our area.
Than there are the pest species like in many areas the wild boar, crow, fox, canada goose etc. And species where you need a special permit from your provincial government or a written directive. For example some geese species, marters etc.