This cannot be done, boards are not forums, they are just simple pages, they cannot be attached to wpForo forum access system.

Is it perhaps an idea to register this as a feature request?

I can see the benefit of it for more people than just me :)

I'm sorry, but there is no permission settings for the whole board. You should set the permission for each category and forum.

I'm aware how to do it on a Forum level.

Is it also possible to do it on a Board level so that all the Forums within the Board will "inherit" the Board permissions? (I would say that Board permissions will/should be checked prior to Forum permissions.) 

That's pretty much the only 100% fool proof way to ensure that an admin/mod won't miss out on setting the permissions when adding a new Forum in the future.

Open the current boards, Forums Admin Page.

Edit the Category/Forum and set No Access for those usergroups which you don't want to have access in that Board from Forum Permissions Field:

https://wpforo.com/wp-content/uploads/2016/12/wpForo-Forum-Permissions.png

I haven't seen anything pointing into this direction yet on the overall or board settings pages so I think this is not yet available out of the box. Is there perhaps a snippet I could use instead for this?

What I want to do is... I'd like to limit the access to a board for exclusive usage by moderators and admins.

And another board with the admins, moderators and a handful of users which I'd like to assign to a custom secondary usergroup for this purpose.

So access limitation on (secondary) usergroup level would do for me.