So is Goju-ryu a martial art or a martial science? I think it defies your neat classification as indeed many other arts probably do. The emphasis on self-improvement or self-defense varies by school and teacher instead of art/system.
How one teaches a system is not relevant to a classification of the ysystem if that person has deleted elements or added elements not generaly accepted as part of the system. It simply changes what that person teaches.
Again , as I said I would not presume that everyon would accept my classifications, since I basicaly made them up based upon experiences. Among them: Speaking to a former Israeli soldier about 20 years ago before Krav Maga became Mass marketed and I asked about the Martial Art of Krav Maga, He said "What Art? There is no art to kneeing someone in the nuts. " Or Peyton Quinn at his Rocky Mountain Combat Applications training center who maintians that he does not teach a martial Art.
For clarity to others that may not have read the article, A Martial Art would include Martial Science as part of it's elements, so you needn't say it is Martial Science but not art. From What you said the ssystem contains the neccessary elements, although youmay choose to train otr emphaisze the science parts.