Months ago when this research was showing up (not on HN) there was a disclaimer that the benefit differed for Shingrix vs Zostavax (discontinued in the United States around 2017), and that Zostavax was shown to cause these benefits (Wales study for example).
Shingrix had a potential side effect of Guillain-Barre https://en.wikipedia.org/wiki/Guillain–Barré_syndrome#Vaccin...
It's interesting that the linked article references, in different terms, the distinction, obliquely. Zostavax is attentuated; Shingrix recombinant.
"Our findings suggest that live-attenuated HZ vaccination prevents or delays mild cognitive impairment and dementia and slows the disease course among those already living with dementia."