This seems like a classic case of correlation vs causation (I only skimmed the abstract). Let’s hope this doesn’t turn into another tabloid article.
Then again, I'm pretty far from a scientist so I'm just spit-balling here.
Not true; I'm sure there is a relationship between age and prevalence of dementia, but it's far from a guarantee.
I've known too many centennials of surprisingly sound mind, and they eventually start having falls and the body can't heal sufficiently to fully recover.
Once the dementia sets in, though, that's another story. The aging process seems to advance quicker when dementia is present.
https://www.nature.com/articles/s41598-022-11427-x
(Unfortunately it increases the risk of some cancers, too.)