The more probable scenario would be that humans destroy the foundation of their own food chain until the population starts to decline in a catastrophic manner. But that seems to be the case for any type of mammal that experienced a significant population grow.
Of course human with their adaptability would damage a lot of biodiversity in the process of "dying out".
The truth is that Mars and Venus are comparatively "shit" even while fitting some conditions as "worlds like Earth", even if their signatures while being swallowed by a white dwarf would be very similar.
But the article is true and there could indeed be a lot of other blue marbles given the size of the cosmos.