It is a new phenomenon when the the thing that goes extinct is critical infrastructure (e.g., pollinators). We've seen similar things with the great potato famine: a critical resource went (temporarily) extinct due to blight, and the results were catastrophic. The paper is trying to make the same statement with minerals, but at a global scale, not just referring to the poor in one country in the 19th century.
I'm not sure the potato famine is the best example, as a large part of the "famine" was due to British mismanagement/cruelty. The Brits kept exporting food from Ireland in spite of the famine, leaving the Irish to starve. Had they banned exports, like India is doing now for wheat, it likely would have been a historical footnote.
They also insisted nobody gift food to the Irish in excess of what the queen of England was giving them. Censored I think...Ottoman Empire's gifts this way. They had to maroon ships full of grain by accident, and tons of people sent food, like even Kenyans and Native Americans.
Ireland still hasn't repopulated. Still half its 19th century peak population roughly.
#/media/File:Ireland_population_change_1841_1851.png){kind=link}
But as a response to the paper, I just think it's a hard argument to make that there are specific material limits to economic growth.