This is probably a key sentence: "...the effect of actually receiving the HZ vaccination was a 3.1 (95% CI: 1.0–6.2, p = 0.007) percentage point reduction in new diagnoses of MCI over 9 years."

MCI = mild cognitive impairment

What's interesting to me is that the effect doesn't appear to be specific to Alzheimer's--rather they see a reduction in all forms of dementia diagnosis.

I suspect the thinking is something along the lines of ... dementia is either caused or heavily influenced by inflammation. Reactivation of HZ virus causes neurological inflammation. So, HZ vaccination is gonna prevent some forms of inflammation and help you avoid dementia--a little bit.

FWIW, I'm trained as a molecular biologist and have a some knowledge of clinical trials, dementia, etc., but I am far from an expert on this.