The paper describes the methodology: for broad analyses like this you’re looking at whether people in the test group died at a higher rate than their demographics would otherwise suggest rather than digging into an individual patient’s details.
“Deaths induced by compassionate use of vaccines during the first COVID-19 wave: an estimate”
“We estimated the worldwide in-hospital mortality attributable to vaccines use by combining the mortality rate, vaccine exposure, number of hospitalised patients, and the increased relative risk of death with vaccines.”