I can't say. I think the whole system will last longer than is commonly supposed among people talking about peak oil and so on. But countries and systems do collapse, like Hemingway's "way you go bankrupt... slowly at first, the suddenly all at once." The Soviet Union comes to mind. But the various European empires are another example.
Collapse is a process of centuries. No Roman looked out their window one day and said, "hey, where'd the empire go?" There are long periods of stagnation with sudden drops, and everyone saying, "well this is just temporary, things will pick up soon." Change, both good and bad, is often talked about for years and then happens surprisingly suddenly.
It's trivial to look at how much oil - or coal, or aluminium, or whatever - the Western countries consume per capita, then multiply that by the population of China and India and so on, and realise we'd need several times as much of those resources as we're currently producing. And it's just not possible.
What it comes down to is that we can't have infinite growth on a finite planet. At some point we come up against limits; as I said, later than the peakers usually suppose, but quicker than most here would suppose.
I would note, however, that your graph is of "absolute poverty", which isn't defined on the graph, but I assume it's one of those "less than two dollars a day" sorts of things. We won't necessarily have more people living in that sort of poverty, but we will have less people living in luxury. And that includes most of us - certainly anyone who's FIREd. I mean, "retirement" is a relatively new idea in history, and relies on a huge energy surplus...