Seems like that article is only addressing the shield tab in an XLR connector itself, not the shield in the cable that the OP is asking about. Even then, it sounds like they use it as the way to ground the wire mesh, which is what I do, too.
Just to be clear, I consider the wire mesh as the shield, not the foil that he is also asking about. Although, it's simple enough to ground the foil mechanically, even if it's not easily soldered. (A mechanical connection between mesh and foil is probably actually inherent in the cable construction.) When one works with antenna cabling, the wire mesh and foil are pulled back to both make mechanical contact with the F connector outer shell. As I stated above, it seems reasonable enough to ground it in a headphone cable, even if there's no way to do that at the headphone connections to the cans.
It ensures a path to ground for stray signals and interference that might penetrate the signal cable wires.
EDIT: It's also a damn shame to waste all that "shielding" technology and construction in a quality cable bundle, by not using the shield/foil. I see so many posts about cables where people simply rip out the multi-conductors in a Mogami or Canare cable so that they can braid them. It think that's a huge waste, just to make something look pretty.
I think you know this, but try braiding some individual conductor wiring to make a pair of RCA interconnects. Then try measuring the response in even a normal environment compared to a pair of properly shielded RCA cables. Even RMAA testing will show this up as a huge difference in noise. Heck, the interference can be plainly audible in a pair of headphones if you connect a DAC to a headphone amp with unshielded RCA cables and there's other electronic equipment nearby.