It wasn’t the initial disappearance of all internet connectivity in itself that wiped out the human race.
Granted, the sudden annihilation of money caused riots that led to the early demise of billions of individuals. The very small percentage of paper money that still existed rapidly lost all meaning.
The few survivors who were able to reinstate a barter system were in turn severely affected by the food shortages and pandemics.
But the human race was not at that stage completely extinguished.
What really hammered the nail in the coffin of this species on the brink of extinction was the gradual realisation that they would never be able, ever again, to stream funny videos of kittens falling in a fish tank or brawling Russian drivers caught on dashcam.
Mass suicides brought an end to lives that were no longer worth living.