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You've assumed that the vaccine reduces transmission risk, which is not the case:
I'm not surprised when I google the author of that paper, it's a bunch of antivax nonsense because the idea that the mRNA vaccines didn't reduce transmission is one of the dumbest I've heard yet. Here's a slightly (ha) better study investigating the matter from real scientists;
https://www.thelancet.com/journals/lanwpc/article/PIIS2666-6...
> Full vaccination of household contacts reduced the odds to acquire infection with the SARS-CoV-2 Delta variant in household settings by two thirds for mRNA vaccines and by one third for vector vaccines. For index cases, being fully vaccinated with an mRNA vaccine reduced the odds of onwards transmission by four-fifths compared to unvaccinated index cases.