This is more of an /r/askscience question.

First, this study was tracing mitochondrial DNA (mtDNA) haplogroups. mtDNA is special because we ONLY get it from our mothers. It's a very small (16,000 bases) piece of DNA present in in mitochondria (the engine of the cell) and sperm don't have them, just eggs. because we only get it from our mothers, and because we only have 1 copy of it (unlike chromosomes where we have 2 copies of each) it is easier to study.

Halpotypes (or halogroups) are sets of differences in the DNA that people share. Broadly speaking we could say there are certain variants that all (or most) people that belong to a certain ethnic group have. You might think of this as a genetic finger-signature, that tells you what ethnicity someone belongs to (this is wildly simplistic but broadly true!).

So what this study did was sequence a bunch of people from Iceland, and found that some of them had mutations in the mtDNA that made it look like they could be from a north american indian (NAI) population. The variants they found didn't match a NAI mtDNA haplogtype exactly but was pretty close. As the authors state themselve,s they can't conclusively prove this mtDNA came from NAIs, because it could have also come from asia. Fruther, they can't rule out that the mtDNA was introduced to the icelandic population well after the purported time vikings visited north america. So this is interesting evidence but not conclusive. There seem to be little or no followup studies so it is difficult to gauge whether the conclusions are widely supported.

ALL THAT SAID.... your question is "is [it] possible to establish if that genetic lineage can be traced to Inuit, Innu, Beothuk or some other group?" -- Yes, absolutely. The Thousand Genomes project has sequenced (actually about 2000) people to find out what genetic differences can define different populations. Although this work has not been done in far NAI -- it's certainly technically possible to sequence a large number of them, establish a genetic-signature for them, and trace whether their DNA has been introduced into other populations (for example, Iceland). After a fashion, this is what 23 and me, and ancestry.com can do.