The article we're talking about is accessible to anyone with a bit of patience and a decent vocabulary (or the will to use a dictionary). I'm not in the humanities and I had no problem understanding it. I think it's really weird to use this particular article as an example of some kind of disconnect between the humanities and the culture at large.
Pop science is fashionable, but 90% of it is fluff or pure nonsense. The level of scientific knowledge of the general public remains miserably low. Are the humanities doing so much worse in engaging the public? This is not obvious to me.
I'm confused now about why you brought Feynman into this. Initially, you seemed to be contrasting successful pop science with unsuccessful attempts by the humanities to communicate with the general public, and suggesting that humanists should ape the communication style of Feynman and other famous scientists. I found this odd, since humanists communicate with the general public all the time, to a much greater extent than most scientists. Just read any high quality newspaper or magazine and you'll find lots of accessible articles by humanities professors, authors, critics, etc. (The article we're talking about is one example!)
Perhaps it would help if you could just give an example of some work in the humanities (not necessarily recent) that you actually like. Presumably you don't think that there's never been any good or accessible work in the humanities. So rather than pointing to Feynman, why not tell us which humanists other humanists should be emulating?