I haven't read this paper yet, but, as I pointed out recently, the numerical superiority of a population A over another B does not necessarily mean that B went extinct; it could just as easily have been fully absorbed.
This paper refers to modern humans and late Neandertals in France, so it is not entirely relevant to modern-Neandertal admixture, which, if it occurred, must have taken place in Asia, to account for the relative uniformity of Neandertal admixture across Eurasians.
Nonetheless, if modern humans outnumbered Neandertals when that admixture did take place, then this would give us a way to estimate whether it was sporadic or commonplace. For example, a 4% Neandertal admixture and a 10:1 modern/Neandertal population ratio would suggest that about "half" the Neandertals were absorbed, and admixture was commonplace. If, on the other hand, the two species had similar population numbers during contact, then the low Neandertal admixture estimates are consistent with sporadic, uncommon admixture events.
Science 29 July 2011: Vol. 333 no. 6042 pp. 623-627 DOI: 10.1126/science.1206930
Tenfold Population Increase in Western Europe at the Neandertal–to–Modern Human Transition
Paul Mellars, Jennifer C. French
European Neandertals were replaced by modern human populations from Africa ~40,000 years ago. Archaeological evidence from the best-documented region of Europe shows that during this replacement human populations increased by one order of magnitude, suggesting that numerical supremacy alone may have been a critical factor in facilitating this replacement.