No, nobody who knows anything about the history of life on earth or the diversity of life now says anything of the sort. How do you suppose the earth could warm so much that tropical species would fail to survive even at the poles (presently, mean temperature differences are over 40C!)? Or, if we get tipped into an ice age instead, notwithstanding the fact that the Earth already went through a dozen or so glacial maximums and four other major ice age periods (which we are in, incidentally), how would this kill off animals living around geothermal vents?

The entire article is full of misinformation. The Permian extinction was the worst, not the Triassic. Humans will only go extinct by 2100 if we manage to nuke each other to death, not directly from climate change (we live in climates that vary in mean temperature by ~30C already).

Climate change has the potential to be the worst human-inflicted calamity that humans have ever suffered. However, there is an immense gap between that and extinction of the human race, and an even more immense gap between that and the end of life on earth.