I think this article misses a few angles. Well, first off, I think it does a great job of looking at it from a few different angles and from a reasonable perspective. I think there are more angles that could be looked at, though it would have bloated the article if they went into everything.
Their assessment that plastics are more environmentally friendly is based on fossil fuel usage and energy usage. Plastic is cheap to make and light, so it uses less energy and less fuel to transport it compared with cardboard or especially glass (one of my pet peeves of packaging is putting a plastic bag inside a cardboard box when they could have just had the plastic bag).
However, they don't discuss other impacts such as microplastics. Glass and cardboard aren't flooding our environment with plastic particles. Another thing to consider is those lined cardboard boxes being sent to landfill are a form of carbon capture. Does it change the balance of whether plastic is environmentally friendly? Maybe not, but it wasn't looked at.
On another related note, I remember being a kid and hearing that the council was looking at stopping recycling because it was no longer cost effective. Up to that point I had thought we recycled because it was the right thing to do, not because people made money from it.