I cannot find much info on this monument besides this wiki link. Stating that it was discovered by an archaeologist named Thomas E. Lee who was taking an anthropological expedition to Ungava in 1964. Also stating apparently how Inuit traditions say no one knew who built it and they believe it predated their arrival to the area. Lee thought it looked European in appearance so he considered it proof that the Norse inhabitated the region about a thousand years prior.
Exactly how popular were building stone cairns among Europeans during the time of Norse settlement in areas like Iceland and Greenland?
Put it simply: I don't believe so, and neither almost all of the specialists in Old Norse religion would not argue for its authenticity, I suppose.
It is true that the Norse settlers both in Greenland and in Iceland had a stone cairn tradition, but it is generally very difficult to date such a cairn, very often with any associated oral testimony who or when they had built, with certainty.
To give an example, The linked blog entry of the Icelandic tourist company collective, Guide to Iceland, includes several pictures of the old cairns, but I'm not sure how many of them could actually date back to pre-Reformation Middle Ages, let alone pre-conversion settlement period. It is also noteworthy that none of them resembles the 'European style' stone cairn in Canada, cited in OP.
While Þórr certainly seems to have been popular among the settlers in Iceland, based on the later traditions like the Book of the Settlement (Landnámabók) (Cf. Gunnell 2017), extant iconographic material of Þórr and Mjöllnir from pre-Christian Scandinavia is not so many (actually very few of them come from the Old Norse settlments in the North Atlantic), and again none of them looks like the cairn in question.
This illustration carved on Altuna stone (U1161, 11th century) from Sweden is arguably one of the most uncontroversial figure of Þórr with his hammer, but is should also be emphasized that the hammer head piece in the illustration is almost exactly the T-shape contra somewhat bec de corbin/ faucon like shape of the cairn in question, though I'm neither specialized in archaeology nor in Old Norse iconography per se, so you shouldn't trust my observation. Another possible iconography of the big hammer is found in Stenkvista Stone (Sö 111) in Sweden, but this illustration is also T-shape again.
(Added) Relative uncontroversial and swift acceptance of L'Anse aux Meadows after its identification (see my previous posts in When did the Norse settlement of North America as being pre-Columbus become settled as a historical fact?) mainly owed to the presence of smaller Old Norse style more daily objects like fastening pins and spindles, not only the resemblance in basic building structure.
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(Edited): corrects typos.
