Right, that is their conclusion but the data don't match. 61% of infections in the elderly are breakthrough even though 85% of them are vaccinated. They are saying that vaccinated don't transmit, but they are using models and assumptions to do that.
As far as I could tell, there was no controlled experiment to figure this out.
The only hard facts in that paper I could see is that the vaccines are a minor help for the elderly.
Define help. Is help prevent symptomatic infection or is help prevent hospitalization and death. I think if you ask the elderly they’ll tell you the vaccines help.