The Truth About Vaccines, page-9063

OK - first up, you conveniently left out the conclusion:

Conclusions: No concerning pattern was noted among death reports submitted to VAERS during 1997-2013. The main causes of death were consistent with the most common causes of death in the US population.

Second: why oh why does nobody ever read past the abstract? If you read the actual manuscript, you'd see that this line from the abstract: "For child death reports, 79.4% received >1 vaccine on the same day." while incredibly poorly worded, is actually referring to the day of vaccination, not the day of death. From the body of the paper:

The median onset interval, the period from vaccination to death, was 3 days (range, 0–2442 days) for all ages, 2 days (range, 0–1478 days) for infants (<1 year of age), 5 days (range, 0–2442 days) for children 1–17 years, and 3 days (range, 0–2011 days) for adults (≥18 years).

Translated, that means that half of the reported deaths in children happened within 5 days of vaccination, while the rest were anywhere between 6 days and 6.7 years later - a testament to just how conservative the VAERS really is in watching out for potential problems.

Now, to understand the reason why none of this is remotely concerning, you have to consider the background rate of deaths unrelated to vaccination. VAERS received 2149 reports over a 6 year period, or 360 per year. If we focus just on the child age group, it was 1469 (245 per year), more than half of those under the age of 1. Now, there are about 80 million children in the US (https://www.statista.com/statistics/241488/population-of-the-us-by-sex-and-age/), and the background death rate is around 685/100k per year for ages 0-1 and 30/100k per year for ages 1-17 (https://www.cdc.gov/nchs/data/dvs/MortFinal2007_Worktable23r.pdf). That's about 35,000 infant deaths per year and 23,000 more in the 1-17s. Grand total of about 360,000 in the period covered by the report. That's not a surprising number - on the contrary, death rates in infants and children have come way, way down since the advent of modern medicine and vaccination.

Put another way, that's a background death rate of 63 deaths per day in the 1-17 age group. Now, let's say for the sake of simplicity that each child gets vaccinated once per year (we all know it's more complicated than that, but it's enough for our purposes here). That means about 0.9 deaths per day can be expected by pure, random chance to have had a vaccine within the last 5 days. Over the 6 years covered by the report, that's 1,950 deaths that are expected to be coincident within 5 days of a vaccine with no actual causality. From the report, the actual number was 1,221 (half of 2,442).

The upshot is that the conclusion of the report is justified - there is no evidence here of "death by vaccine". On the contrary, it shows they are stunningly safe - with tens of millions of vaccines administered in the US every year, there is no evidence in these statistics to suggest any deaths whatsoever caused by them.