The article says that one possible reason the vaccine protects against dementia is incidental protection from other diseases. Getting chickenpox as a kid might protect you against shingles, but maybe not against those other diseases.
Getting chicken pox as a kid means you already have the H. zoster virus in your system, and when you get older as your immune system weakens, it may come out for a second go around, manifesting as shingles. Having had chicken pox as a kid is one of the reasons why I got my Shingrix as soon as I was able.
No! The opposite thing is true. Getting chickenpox as a kid drastically increases your likelihood of getting shingles as an adult. The initial chickenpox infection is the mechanism by which you're set up for shingles: you get it, fight it back, and it remains dormant in your nerves. Shingles is not simply chickenpox; it's the secondary infection you get from a resurgent zoster outbreak based in your nerves.
Don't get chickenpox.