The numbers are optimistic, but in principle this is not wrong. The lithium atoms don't disappear, they're still in the battery and can be recovered. Yes it's difficult and requires energy, but no more so than extracting it from natural ores. The batteries degrade, but the minerals do not.

But the total amount of lithium available in the earth's crust is not the problem right now. The problem is the processing and refining capacity that we currently have, which is not enough. Battery recycling is essentially the same problem as refining, but with some added steps, so it's not the solution right now.