How about some percentages rather than "high proportions" and "significant"? The other articles I saw on this claimed this meant that most of the diet was meat with some plants. This article seems to imply a large amount of plants.
However, “the study is really exciting,” says Henry, author of the earlier study of Neandertal dental plaque that showed that a Neandertal in Iraq ate plants. “If they are correct, this is one more nail in the coffin for the idea that Neandertals were obligate carnivores.”
Obligate carnivores? Who could look at the teeth of a neanderthal or modern human and consider them "obligate carnivores". We have omnivores' teeth with a mixture of incisors, cuspids and molars unlike a cat's teeth. Also the typical view of early humans is as hunter/gatherers. The gatherers weren't just picking up meat... they gathered plants. And modern humans aren't able to produce certain chemicals they need which can only come from plants, and I expect that neanderthals were the same. Vitamin C comes at the top of that list.
It’s in their paper; the reason it has to be portrayed as a huge breakthrough is because of the rather bizarre anti-Neandertal bias and claims that started in the 19th c and persist (especially in England) today.
“Significant”, in a scientific study, generally means the results are above background noise and testing error. So, for example, if noise is 2 (whatever the represents) and error is 1, then a result of 4 or more would be significant but 3 or less would not be significant.