Understanding "BNT162b2 mRNA Covid-19 Vaccine in a Nationwide Mass Vaccination Setting]"

Dear community,

I am having a hard time to understand the statistical analyis in the often-cited work BNT162b2 mRNA Covid-19 Vaccine in a Nationwide Mass Vaccination Setting and I was hoping that you can assist me.
My question is about the measurement of the effectiveness of the Covid-19 vaccination. In the paper it says

For each period, we used the Kaplan–Meier estimator with daily outcome and censoring events to compute the probability (“risk”) of the outcome during the period, using matched pairs in which both persons were still at risk at the beginning of the period. We then calculated risk ratios for vaccination as compared with no vaccination and estimated the vaccine effectiveness as one minus the risk ratio.

What exactly is done here? When calculating the risk ratio isnt’t that the same as calculating an odd ratio? And why is the counterprobability calculated?