No.
If you read the original, rather short article you'll notice that it never makes any kind of claim about the vaccine destroying any protection. To the contrary, the article argues that the data supports booster vaccinations for children.
Reuters has done a fact check of this claim which includes quotes from the original author of the study.
“The statement that ‘the vaccine destroys any protection a person has from natural immunity’ is unfounded,” Lin told Reuters in an email. “Our data showed that the vaccine was effective against infection for 4 months. In addition, vaccination conferred greater protection against hospitalization than against infection. Finally, no vaccinated children died whereas 7 unvaccinated children died.”
So the author of the study used to make this claim directly refutes it.
In both figures, the lines’ continuation past the boundaries of the graph is strictly an illustrative technique, to show the overall trajectory more clearly, according to Lin. They do not indicate that vaccine effectiveness becomes “negative” at any point, or that children become more vulnerable to infection than they would be without vaccination, he said.
I really dislike these graphs, they don't show clearly which parts are actual data points and which parts are interpolated or extrapolated. But no matter how bad these graphs are, according to the author they are not intended to show that the vaccines reduce protection, that is simply an extrapolated line and not measured data.
As for the graphs C&D the major flaw seems, they are very hard to be thatread in my opinion as they completely omitdon't clearly indicate which points of data were measured (which are fewer for the vaccinated case than for the unvaccinated case, so the timeframe observered is different in both cases). The error bars are also somewhat confusing as there is also the shading for the prevalence of the different mutations in the background. I created a very rough plot myself from the data in the supplementary material (only for the delta variant) to understand this:
Blue are the unvaccinated, red the vaccinated children. The x-axis is the number of months.
The error bars for the vaccinated children are much, much larger than the error bars for the unvaccinated children. The series also doesn't continue as long as it does for the unvaccinated children. The "trend" you see in graph D for the vaccinated children seems to be an extrapolation that is based mostly on the last two data points that have absolutely enormous error bars. This is extremely misleading and not at all what the raw data shows.