Neil Price, who was interviewed for the National Geographic article you've linked, is probably the strongest voice for gender imbalance as a factor in Viking-Age history. Other notable voices have included James Barrett [pdf] and Nancy Wicker. There's two basic ideas at play: (1) Viking-Age Norse culture encouraged female infanticide, that is, parents would kill female infants who were expected to bring little wealth or honor to the family, and (2) women were prime targets for slave raiders and traders, thus becoming concubines, wet nurses, textile producers, and domestic servants of all sorts. It's also worth mentioning Mats Roslund, who has deduced that imported [Slavic] women were probably responsible for producing most of the day-to-day pottery of late Viking-Age Scandinavia.

The article posits Irish DNA among Icelandic women as a particular indicator that vikings needed and therefore stole women in mass quantities. I'm personally not keen on using Iceland as our basis for understanding Norse cultures elsewhere, since Iceland was such a unique branch from the broader Norse milieux. It's also difficult to judge when the 'Celtic' DNA entered the Icelandic genetic pool, since many early settlers came via Ireland or the Scottish isles. That is to say, Scandinavian males who went a-viking self-selected to join societies that were male dominated, and many of them likely settled down with local women (force was certainly involved in at least some cases) before heading off to be Icelandic farmers, bringing their women with them. Alternatively, perhaps some of the free Norwegian women who migrated to Iceland were the daughters or granddaughters of Irish slaves who had been carried forcibly to Norway. Either way, the DNA evidence doesn't actually tell us when or where the gender imbalance occurred, or whether it was a pervasive factor across all of Scandinavia throughout all of the Viking Age or whether it was something caused by the male-dominated behavior of viking raiding itself.

I'd encourage you to read the original scholarly arguments, but my general impression is that the other evidence is similarly ambiguous. On the one hand, at least some Norse are known to have practiced female infanticide, perhaps causing local imbalances that may have been a factor driving some young bachelors to seek female companionship through violence or trade. On the other hand, easy access to cheap female companionship (at least if we trust the written sources) probably meant that men of means might have taken little note of gender imbalances, and that even if gender imbalance was occasionally an individual or even a local factor in historical processes, there's no reason to assume that it was a systemic problem affecting large numbers of historical actors.

That sidesteps your question about polygamy, mostly because I don't think that the evidence is there. The Icelandic sagas describe some men who joined with several wives and concubines, but some sagas also describe women [see Hallgerður] who survived several husbands. Female infanticide may have caused a general imbalance, but it was probably offset but the opportunity for individuals or communities to acquire women through the slave trade. If this is the case, we could expect poorer freemen to have acted out of a need to acquire women, whereas more well-to-do elites might have used their access to women as a means to control their free farmer clients. Scholars have yet to demonstrate whether this was, in fact, the case. It remains an open question.