Obviously there are confounding variables besides vaccination status, but I find it pretty compelling that the decrease in COVID mortality among the vaccinated group was significantly larger than the decrease in all-cause mortality of that group. This suggests whatever the difference was between the two groups, besides vaccination, either had a much larger impact on COVID than other causes of death or that the vaccine had some positive impact.
One example of the former explanation I could imagine is that people who got vaccinated against COVID were probably also more likely to take other preventative measures, like wearing a mask or avoiding larger crowds of people. Those precautions would be more likely to be effective against a contagious disease like COVID but less likely to protect them against some other causes of death like heart disease.
I'm not sure how likely I find that as an explanation compared to the alternative that the vaccines provide at least some level of protection. My observation was that widespread measures specifically meant to defend against COVID, like masking and social distancing, largely went away well before the end of the time period covered by this study, at least in the US.
Amusingly, I suspect the anti-vax contingent would likely be bothered by data suggesting anything the COVID vaccinated group was doing differently protected against COVID, since their position seems to largely be that not only is the COVID vaccine useless, but so are any other measures meant to reduce the spread.