TL;DR: Battery demand grows. Best current tech uses nickel and cobalt. Their prices grow and at the current growth trends demand outstrips supply within 20 years. We should fund research (in the author's area) to find better alternatives (e.g., using iron and silicon). This is valid but not surprising and hardly catastrophic. This is not "10 years left to find an alternative". But what turned me off is scaremongering…
I don't know of any laptop today that's using a nickel cobalt battery. Those ones usually allowed you to remove the battery pack from the laptop. Now there all based on lithium-polymer now. Same with smartphones.
I did some research in lithium polymer batteries a few years back. I distinctly remember there being almost 10 or so variations of lithium polymer mixes being used in battery production.