@kev-m I figured this out. I was looking at the Global permissions and not the category specific permissions. To change the category there is a dropdown menu on the upper right hand side of the Manage>Privileges page. Then I select the category and remove the guest permissions.
@meetdilip: Yes, of course it depends on the different sites. It should be an optional, configurable feature. Since it seems to be not yet implemented in NodeBB, I woud like it to be considered a feature suggestion.
About choosing Discourse or NodeBB, Discourse has already very nice features like this self-moderation. However, for some other points that can be important depending on the site, NodeBB gives more options. For example, Discourse has explicitly discarded pagination as a possible option, therefore infinite scroll must be used in all cases. Also adamantly discarded are hierarchical categories, and only one level of subcategories is allowed in all cases.
On the other hand, NodeBB seems more open to give options for users' suggestions, such as optional pagination, unlimited subcategory levels, flexible theming, etc. So, this project probably will use NodeBB.