The article you cite was written, not by a health care professional, researcher, or biologist, but by a disgruntled former CDC employee, with the assistance of a political activist. The computer scientist author seems to have misunderstood the science behind the numbers and wrongly believed that there was a conspiracy taking place in his workplace. Bless his heart. Apparently the legitimate scientific journals refused to publish his article, so he paid to have it printed in Annals of Clinical Pathology (which does not meet the scientific standards required of MEDLINE indexed journals). Perhaps that is why the biology does not make any sense.
Shingles is a specific illness with only one cause. When the Herpes Zoster virus, which hides in the body after a person has chicken pox, is allowed by the person's immune system to reinfect them, the person develops the nerve inflammation known as Shingles. Usually the inflammation resolves (and it can recur), but sometimes the person is left with permanent nerve pain (post-herpetic neuralgia). You cannot get Shingles if the Herpes Zoster virus is not already hiding in your body. You have to have had chickenpox first. That is why children with immunity to chicken pox due to the vaccine are unlikely to EVER get Shingles - in almost 99% of them, the virus never gained a foothold in their bodies (about 1% of children who get the vaccine develop a mild case of chickenpox). Sometimes when a person receives a vaccine, their immune system fails to respond to it. For this reason, titers are drawn and nonresponders are immunized again. Failing this, those people would be susceptible to wild chickenpox, and later, to Shingles.
A strong immune system keeps the Herpes Zoster virus locked down. Shingles in children has always been extremely rare, occurring only in children who are immune compromised, such as those undergoing cancer treatment. Because (thankfully) there are more and more children who are cancer survivors every year, we should expect those numbers to increase. However, if they were vaccinated prior to developing cancer, most are not susceptible to Shingles, because the virus is not hiding in their bodies. Most cases of Shingles occur in older adults who had chicken pox as children and whose immune system is naturally weaker and also has gradually "forgotten" to defend itself from the virus. There is a legitimate concern that now that wild chickenpox is so rare in the USA, the immune systems of adults with the virus hiding in them are no longer being "reminded" to defend themselves, because we are not being exposed to the virus at the grocery store and in other public places. This is why it is such good news that there is a new extremely effective vaccine against Shingles.
The CDC does not believe that the increase in Shingles cases in the USA can be fully explained by the lack of naturally occurring "boosters" (exposure to children with wild chickenpox) because they look at datasets OTHER than the ones Mr. Goldman was hired to analyze. Shingles incidence is increasing in the USA, but it is increasing equally in countries where the Chickenpox vaccine is not widely available. In addition, the percentage of people in the USA who are immune-compromised is rising as people live longer and are active in the community despite taking strong immunosuppressant medications. If these people have Herpes Zoster hiding in their bodies from an encounter with chickenpox (usually as a child), they are at high risk for developing Shingles.
Bottom line: Before the chickenpox vaccine, virtually 100% of the population was at risk for eventually developing Shingles. The chickenpox vaccine does a lot to prevent Shingles (~99% of those vaccinated with it do not have the virus hiding in their bodies). It is possible it slightly increases the risk of Shingles in unvaccinated people because they are not being exposed to the virus in public places. Fortunately, as of this year, we have a Shingles vaccine that is extremely effective at preventing complications from Shingles such as post-herpetic neuralgia.