This is a controversial point in art theory.
"Controversial" indeed. The theories of Art pour l'Art and Formalism developed initially as a rejection of the notion that art can or should be judged upon non-Art external elements such as narrative, theology, morality, etc... The average member of the art audience during the Renaissance would not have questioned the idea that a painting might be deemed "poor" if it did not meet certain expectations in terms of religious expression, morality, etc... With the late 19th century, this idea was called into question. It was suggested that art might portray subjects or themes that were deemed ugly, inappropriate, unsavory, or even bland... and yet if the form in which these were realized was fine enough, such work might still qualify as "good" or even "great" art.
You naturally know that in the art scene of the 19th century, historical, mythological and religious motifs became more and more disputed by artists who believed in the autonomy of visual art, that is, in the independence of the artistic expression from things that haven´t anything to do with painting in itself.
Initially, the rejection of historical/mythological/religious themes had more to do with the artist's efforts to create an art that spoke of the "modern world".
The first to rebel against the traditional idea that painting has to transport non-visual contents were the Impressionists who reduced these contents to an extreme superficiality - that is, the viewer was not in need of knowing a wider cultural context of the shown scenery because he or she knew it from everyday life...
I would avoid assigning the rejection of non-visual elements to any single group of artists or period. Rubens was painting landscapes that had no higher narrative meaning in the 1600s...
The same was true of Gainsborough, Turner, Constable and numerous others...
Artists like Chardin and Zurbaran focused on the humble still life... which were essentially motifs for painting...
And artists like Vermeer and Boucher frequently focused upon scenes of everyday life:
Vermeer often repeated such motifs to the same degree later employed by the Impressionists... until it became something like a theme and variations in music...
The next step was the Expressionism which reduced the objects to half-abstract shapes.
While Expressionist distortions might have been primarily formalist to some artists... pointing the way toward total abstraction... this certainly wasn't true of many of the Expressionists... especially not Munch or the German Expressionists.
For these artists, formalist innovations remained a means to an end... a means of wrenching further meaning out of their chosen themes/subjects.
Kandinsky made the next and final step to abstraction using only colors and forms to express the basic visual energies, being inspired by music as I wrote before. Some years earlier, the artists Hilma af Klint and Frantisek Kupka created the first abstract paintings, both of them unfortunately remaining rather unknown in spite of their pioneer work.
Remember, that Formalism and Abstraction were not unchallenged in the 20th century. The German Expressionists, Surrealists, Magic Realists, Social Realists, Mexican Muralists... and even Picasso would have called these notions into question.
So, radical advocates of the idea that painting should be basically independent of non-visual content would argue that the artificial value of - for example - the pictures shown in your article are only to be measured by the visual expressivity, independently from any historical or cultural background information.
Such is the theory of Greenbergian Formalism... but it was not universally accepted. Even leading figures of Abstract Expressionism (especially DeKooning and Guston) questioned the notion of removing narrative and non-art elements (the subject matter) from art. While one may embrace a film as primarily visual (2001, A Space Odyssey, comes to mind) one would never suggest that the non-visual elements present in a film were not of importance in understanding and even valuing a film. The same is true of painting. Any element present is of importance in fully understanding the work.
It would be pretentious of me to suggest I fully understand these works of art...
...based solely upon my notions of art rooted in Modernist Formalism. It would be no less pretentious to suggest I fully understand a Baroque narrative painting without having the least knowledge of the narrative employed or the tradition in which the work was created.
So it is one thing to ´understand´ a painting and another thing to appreciate its articifial qualities. What is needed for understanding has nothing to do with these qualities. For example, to appreciate the quality of Rembrandt or Rubens or Leonardo or Caravaggio paintings, one needs no historical or religious or mythological background info. Moreover, in my view such info does not add anything to the artificial value of those paintings.
Yes... I can "appreciate"... "like" a work of art that I don't understand... we all bring prior knowledge of our own... prior experiences... to bear upon any work of art... yet it seems only logical that a greater understanding of a work will likely increase the appreciation... although the reverse is also possible.