No, but it's all sugar. Here's a concise list of sugars: https://www.thekitchn.com/whats-the-difference-muscovado-145157

That recipe seems overly complicated. The demerara "for rolling" is for rolling the cookie in as a topping? For rolling out the shortbread on? For the former, you could use any kind of finishing sugar you like, including colored, raw sugar, brown sugar. For the latter, you might want something closer to the real deal, like maybe mix larger crystal raw sugar with some brown sugar for the molasses flavor.

Especially now, when getting specific sugars might be an issue, I say just wing it with what you have. There are subtle differences in flavor and texture, but it's still just sugar. :)

Sorry I didn't include the instructions. The formed cookie dough log is rolled in demerara sugar before slicing.

• Using
  an electric mixer and a medium bowl or a stand mixer fitted with the
  paddle attachment, beat butter, granulated sugar, brown sugar, and
  vanilla on medium-high speed until super light and fluffy, 3–5 minutes.
• Using
  a spatula, scrape down sides of bowl. With mixer on low speed, slowly
  add flour, followed by chocolate chunks, and beat just to blend.
• Divide
  dough in half, then place each half on a large piece of plastic wrap.
  Fold plastic over to cover dough and protect your hands from getting all
  sticky. Using your hands (just like you’re playing with clay), form
  dough into a log shape; rolling it on the counter will help you smooth
  it out, but don’t worry about getting it totally perfect. Each half
  should form logs that are 2–2¼" in diameter. Chill until firm, about 2
  hours.
• Preheat
  oven to 350°. Line a rimmed baking sheet (two, if you’ve got 'em) with
  parchment paper. Brush outside of logs with egg wash. Roll logs in
  demerara sugar (this is for those really delicious crispy edges).
• Slice
  each log into ½"-thick rounds. Arrange on prepared baking sheet about
  1" apart (they won’t spread much). Sprinkle with sea salt. Bake cookies
  until edges are just beginning to brown, 12–15 minutes. Let cool
  slightly before eating them all.
• Do Ahead:
  Cookie dough can be made 1 week ahead. Tightly wrap in plastic and
  chill, or freeze up to 1 month. Cookies can be baked 5 days ahead. Store
  in plastic wrap or an airtight container.

I just found a website discussing and comparing different sugars and Turbinado was the top suggested substitute for Demerara.

In a pinch you could also use some light brown sugar spread out and dried....
Turbinado and demerara and different bot close enough as to be interchangeable.