Haven't read all this yet but am saving the link to come back to. Don't think this critic understands the art he or she is calling "formalist."
And possibly confuses the extremes of late Greenberg theory with the studio practices Greenberg chronicled early on.
Greenberg believed that the subjects of the visual arts should be their respective media. Painting should be about paint, and sculpture about the materials of sculpture. It follows that politics and narrative, as extraneous to the art media, debase the purity of visual art. Formalists evaluate art according to physical qualities such as color, size, shape, line, texture, and so on, and treat the ideational content of works as irrelevant. They view themselves as being mainly protectors and upholders of high aesthetic standards.
This is an idiot's view of abstract art and the reasons for doing it. Greenberg was not this unsophisticated, didactic as his later criticism became. To reject verbal narrative, theatrics, etc in art isn't to reject "ideational content." It is to recognize that the ideas of many paintings are expressed non-verbally and require new kinds of metaphors. Greenberg adopted and codified the language he heard artists using in mid 20th Century studios ("push-pull," etc.). Much of this language centered on the properties of media but only hack artists stop there. The ones who wrote, such as Mondrian or Newman, tended to the philosophical. Unfortunately, reduced to writing, you have to deal with such ideas as writing. Trained as a writer, Greenberg had little use for windy bloviation and therefore insisted on what was verifiable or falsifiable.
Abstract art is just as difficult and radical a proposition now as it was fifty years ago, and still drives social critics crazy, such that they have to make its practitioners and advocates into pedants quoting Ralph Mayer's The Artist's Handbook (a text on methods and materials) as some kind of governing philosophy.