No, the science doesn't imply that climate change is going to mean literally everyone dead, only a massive cost to maintain things as they are today. Contrawise, Alexandria Ocasio-Cortez said "the world will end" by 2030 if we don't stop climate change. (Source: https://thinkprogress.org/we-dont-have-12-years-to-save-the-...)
So, yes there are people being absolutely, ridiculously, unscientifically hysterical about the effects of climate change. Unscientific alarmism is just as harmful toward efforts to properly manage the global ecology as the unscientific denial of changes.
We've already witnessed extreme political radicalisation within Western countries as a result of displacement of people from Syria: numbers in the order of a few million. It seems likely that displacement from climate change would be a significant percentage of world population (8+ billion soon). The reaction to that will be apocalyptic.
It tries to counter claims of "4 billion casualties".
This kind of statements is exactly what this article is about.
If the author means literally everyone dead, planet gone, then obviously it won't be "apocalyptic", but the science is suggesting it's likely to be really bad. It seems pretty unreasonable to say "not apocalyptic? oh then that's not so bad, what's all the fuss about" when the situation is this dire. We could avert a lot of it if we actually did anything about it.