This is a common misunderstanding of statistics: your odds of a severe case or death are much lower if you’re fully vaccinated but the size of that population is so much larger that you’ll have more total deaths than the smaller population which has never been vaccinated.
Think of it this way: the odds of a soldier dying if shot are 10% if they’re wearing a bulletproof vest and 80% if not. There’s a battle and afterwards they realize that 20 dead soldiers were wearing body armor and 10 were not. Does that mean armor was bad? To answer that question, you have to know how many there were in both groups: if it was 50:50 that would support questioning the value of those vests but if it was 90:10, the reverse would be true.
The article you linked is well worth reading as it explains this and several other confounds for analysis, namely the higher likelihood for high risk people to get vaccinated even though their failing immune systems still leave them at elevated risk (a vaccinated 80 year old’s risk goes down to a level similar to a 50 year old, not a 20 year old), and the fact that waning immune response and new variants mean that we really need to avoid thinking of vaccination for COVID as a lifetime boolean toggle – someone who got a single dose 2 years ago has a different status than someone fully vaccinated with a bivalent booster.