A piece such as this should engage with the direct cost/benefit calculations that have been done by economists and EAs (e.g. Giving What We Can), which make it seem hard to argue that climate change is competitive with global health as a cause area.
How much it would take to stay under a mostly arbitrary probability of a mostly arbitrary level of temperature change is a less relevant statistic than how much future temperatures would change in response to reduced emissions.
It’s hard to tell where this site is getting its numbers from, but my understanding is such claims are usually based on misrepresenting the RCP 8.5 emissions scenario as representative of business as usual even though it makes a number of pessimistic assumptions about other uncertainties and is widely considered as more like a worst case scenario than a median case scenario.
As far as I can tell, claims that extremely high climate sensitivities are plausible tend to be based on conceptual misunderstandings of Bayesian probability.
The Stern Review isn’t representative of climate economics as a whole and has various problems that you can find using your favorite web search engine.