“A more modest population – gently easing population to 4 billion by 2200 – would protect Earth's natural heritage, including its wild habitats, wild species, and its climate. Such a world is within our grasp,” they concluded.
I think we could easily see the global population drop back to 4 billion well before 2200, but it almost certainly won't be "gentle." Wars, famine and disease, more likely.
For some context, the global population was about 4 billion in 1974-1975, so a little over 50 years ago. It's very natural for a population crash to follow such a relatively sudden population explosion.
The Earth is finite. We do not have infinite resources so we can't grow - in population, production or consumption - forever. We will hit the physical limits to growth eventually, and when we do there will likely be a sudden and dramatic collapse.