OK, pardon my reveal here, but before I was a recording engineer I was a professional classical musician, and the music that this video is about happens to be some of the music that I was particularly drawn to. I recognized the first recording played in the video--the violinist on that record, the late Rudolf Kolisch, was the most influential teacher and friend I've ever had.
I can take a joke, as could Mr. Kolisch and the three composers that the video refers to (well, maybe not Webern so much). But it's a whole other thing if you treat someone's life's work as something that can be dismissed lightly, when they are among the most important composers of their time. And though this little video is a smooth production and not something that can just be thrown together, someone forgot to do their basic homework--about half the pieces in the video aren't twelve-tone compositions. So please don't assume that its smugness has been well earned.
A great deal of the music of Schoenberg, Berg and Webern is very beautiful when it is well played--though beauty isn't all that it, or any other music, is about. I've performed a good many pieces by these three composers; once you get to know it, it's as natural and expressive as Haydn, Mozart or Schubert. And yes, people (who can) definitely do whistle the tunes from it.
--best regards