The article already mentioned that unpaid internships are typically widespread "in competitive and glamorous industries like politics, entertainment, and fashion where there are far more entry-level candidates than jobs available".

And we might add some more: non-profits, the academia, cultural institutions like museums, i.e. the dwellings of those who scorn corporations, capitalism, always put their vote as left as possible.....while having no problem at all to employ interns for shits and giggles, because their loan is that they can contribute to some sort of higher cause.
Having studied liberal arts myself, I know what I am talking about. After all, in one case, it was even too much asked to have a certificate of internship in time, and I only got it six months of insisting and repeated calls. In another case, my university hosted a national historian congress, and instead of employing actual waiters to serve the thirsty academics and who would at least get a minimum wage, they employed students of that university...for 0,00 $ an hour and a certificate that they had "contributed the organization of an important congress", while they could have just as well worked for an event-manager, do the very same thing and maybe even have higher chances of landing an actual job. But that would have been for a corporation, and they are evil, right?
You know a tree by it's fruit, and due to my experience, that of non-profits is the worst of all.

So no, it's not the capitalist society's fault, at least not in many cases. On the contrary: this sort of exploitation all too often arises from abusing young people's idealism, not their strife for profit.