The article is quite chaotic, inhomgenous... amd full of sensational claims far away from the hard ground of reality.
Indeed, a rather strong climatic shock is possible. The most aevere effect would be shifts of clima-zones and a nasty sea level rise. That would or will hit humanity, us. But its.not a threat for civilisation.
450 Chernobyls at once would do a blast. Indeed we are more sensible against radioactivity, than most other animals. Still it would need way more to be critical. Even if combined with clima-shock.
Still our food and livestock will grow well. It wold be more toxic for us to eat and drink, cancer rates would soar up, and genetic diseases too. But neither we, nor the other complex life forms would be in danger.
A full fledged nuclear war, plus clima shock, plus multi-year long nuclear winter... This may be enough. Definitely it would disrupt civilization and infrastructure. Still, most of the other life forms, animals, plants can stand way more, than we. The clima double whack may caus a major extinctoon (see end of the non-avian dinosaurs), but likely it will be less severe = more species survive.
While redioactivity takes the toll on humanity, we are good surviving by being able to eat nearly everything, maybe we could survive but loose most of the technical advance.
Even Ozone layer disruption... Most of earth's species would not take THAT harm. Makes life more difficult, shorter (cancer), harms plant growth, but nothing too critical. Such periods happen ... this was never a mass extinction.
I absolutely doubt that we can burn enough Carbon to destabilize enogh Methane to go combined into an Eozene like warming, with tropical arctics and anoxic seas. Anoxic deep or even shallow seas, this could kill us by poisoning the atmosphere. Still, plants and many species would survive... they did. Muktiple times.