I don't think there's any real basis for that statement.  3.5C warming would very likely set in train some very profound impacts in the long-term, eg. commitment to large sea level rises, and would also shift climate patterns to make some places wetter and others drier, and everywhere hotter of course, and this would increase the risks to biodiversity in many places, but I don't think it can credibly be regarded as an "extinction point" in the way that is described in that quote.  Many (most?) regions of the world would still support life, albeit favouring different species to those currently occupying those areas.

A key point of course is carbon dioxide and its effects on plant growth. The level of carbon dioxide that would accompany a 3.5 degree C global warming is quite uncertain, as we don't know very precisely how strongly the climate responds to any given increase in CO2 (doubling CO2 could lead to anything between 1.5C and 4.5C warming, possibly higher although probably not vastly higher).  The higher CO2 accompanying any given level of warming, the more that some effects of climate change may be ameliorated, eg. by increased water use efficiency.

Richard Betts.