Build context menu for news articles (sample image included)
Not really an answer, but perhaps a lead.  In Drupal 6, a similar thing was accomplished with the book navigation block.  You could have the book navigation block filter to a certain number of steps up/down tree from the node page that you were currently viewing.

I am not sure how this could be accomplished with existing views configuration, as I think tree navigation is not a common thing for views.

This is more the kind of trick I would expect to find in Taxonomy, based on the vocab's hierarchy.  There, navigation can be a more certain thing, as the structure is defined in the vocab, and they are just filling the tree leaves with tagged nodes.  Again with the Drupal6 reference, but perhaps you can scavange code from http://drupal.org/project/taxonomy_treemenu

If you do code something, release it back to the community?