According to the New York Times, the new study found that:
[T]here was approximately the same number of adults in the 20-to-40 age range and over-40 age range in both groups. About 25 percent of adult humans and Neanderthals survived past 40.
Infant mortality rates, the proportion of the population that was made up of juveniles, and the fraction of juveniles who survived to become adults is not estimated.
If the number of juveniles at any given time was roughly equal to the number of adults (which is a rough estimate of what one would expect after an initial expansion of a founder population to a stable level), then this would imply a life expectency for children who escaped infant morality on the order of twenty years. This is on the order of half that of the least developed countries today, and probably somewhat below life expectencies in the Roman Empire. Infant mortality then was probably in the 15% to 35% range seen in the the least modern circumstances for which there is good documentation.
Even with infant mortality on the high end of this range, significant child birth mortality of women, and a fair amount of birth order spacing as is found in modern hunter-gatherer societies, one would expect the average woman to have about six children in a lifetime (the highest numbers of children per woman in agricultural world societies today is about eight), two of whom, on average, would die as infants, and only half of the remaining four of which would survive to have children of their own in a stable population. Thus, about two-thirds of children born would live the first year, about one-third of children born would live to age twenty. Life expectency at birth would be something on the order of twelve years.
It is also worth noting for context, that in the hunter-gatherer era, except for a few highly productive fishing societies like those of the Pacific Northwest and Japan, that until farming was invented, "Individual band societies tend to be small in number (10-30 individuals), but these may gather together seasonally to temporarily form a larger group (100 or more) when resources are abundant."
Thus, in a seasonal gathering of half a dozen bands with an average of twenty people each, there might have been 60 kids, 45 adults who were not yet middle aged, and 15 adults who were middle aged or elderly, of whom probably no more than 5 adults would be older than the sixty-five year old age we think of as retirement aged in modern life. One or two bands out of half a dozen would have had no elderly adults, while probably none of the bands would have had more than a couple of elderly adults. If the pre-modern populations that I am most familiar with are any indication, child birth mortality would probably have caused an excess of men over women in among the elders. So, there might only be one or two women among the elderly in the larger tribe.
According to John Hawks, whose post is the first link above, the newer study, however, "found fewer [modern human] older adults in the early Upper Paleolithic."
Hawks engaged the authors of the new study on their decision not to cite the earlier study, but apart from issues of academic etiquette, the result enhances confidence in the conclusion because replication of results is key part of the scientific process.
The research (and their one difference in result) matters because one of the notable hypotheses that has been used to explain the great success of modern humans as a species has been the observation that having a significant number of grandparents in the population may have provided selective advantages for the community as a whole, perhaps, for example, by making it easier for cultural practices and community oral histories to be preserved more accurately for longer periods of time.
If the new study is closer to the truth than the older one, or even if the truth is somewhere in between them, the grandparent hypothesis is not disproven, but it then follows that the grandparent advantage, rather than being a feature of modern humans that gave them a strong edge relative to Neanderthals and other archaic hominins. Instead, this may have been something that arose in most places (the Jomon in Japan whose fishing society was the first to make pottery may have been an earlier exception) sometime after the Last Glacial Maximum of about 20,000 years ago. Thus, it may have arise after a period of something on the order of 200,000 years during which anatomically modern humans existed and had characteristically modern human tool sets, which included, for example, more sophisticated stone work and the use of bone in tools not utilized by other archaic hominins.