> How do you exterminate 7 billion people spread over ~57 million square miles of land?
I mean, just make the earth uninhabitable for humans. There are a few ways to accomplish this; even excluding climate change, nuclear weapons were and continue to be one such specter as the article alludes to.
Sure, some people will continue to eke out an existence even then, but it's quite easy to imagine humanity perishing over the course of a few generations after an event like that.
Also, when people say things like "humanity being wiped out" they usually don't literally mean "extinction of homo sapiens". They usually mean "quality of life significantly degraded" such that life resembles a Mad Max movie more than what we know today.