You can't conclude that from this data.
As the researchers pointed out in their footnote, since many younger people weren't eligible for the vaccine during the data collection period the 10-59 vaccinated population is on average older than the unvaccinated, so you would expect their all cause mortality rate to be higher.
It isn't an apples-to-apples comparison.
It would be nice if they broke down the data a bit more 10-19, 20-29, 29-49 or something.