[0]source: personal experience
https://www.washingtoncitypaper.com/columns/straight-dope/ar...
Or you might prefer this: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4688990/
TL;DR: It's a device whose purpose is to mix the smoke of the cigarette with air which is intaken via the micro holes found on the body of the mixer (a.k.a. "filter). The different air/smoke mix rates give the smoker a different perception of the smoothness / lightness of the cigarette. As a side note, as your first reference mentions, this "filter novelty" may have made things worst as the smoker will make deeper breaths and keep the smoke longer into the lungs when inhaling a more diluted smoke puff.
[0] https://www.theatlantic.com/health/archive/2017/07/cigarette...
Source: Poster on the wall in the Yellowstone NP gift shop.