This seems to be the inverse of a zero-sum game: the West might have got a lot richer, but hundreds of millions of people were lifeted out of extreme poverty at the same time.
Parent's thesis is that it's not a typical zero-sum game, but "a zero sum game with an ever increasing pie". It's an interesting idea; I don't know if there are formalizations of it.
Even if the pie remains exactly the same, it's not a zero sum game: simultaneous value for two people can be created out of nothing simply by the voluntary exchange of goods and services between them while everything else remains the same, see my other comment here for examples:
https://news.ycombinator.com/item?id=33719823
As another example more relevant for this context, poor people can exchange their time for money, which can then be used by them to acquire other things they value more than their time (food, housing, etc).
So yes, poor people can get themselves out of poverty even if the pie doesn't change. There are many examples of this happening (i.e. poor people lifting themselves out of property much more than the pie grows).
But of course, they can do that even better if the pie increases, i.e. if we get better at producing food and housing even more efficiently.
But even if the pie remains the same, value can be created out of nothing by the simple voluntary exchange of goods and services and poor people can also greatly take advantage of that.
It doesn't mean that some people have to lose something when poor people gain something. Both poor and rich people can simultaneously benefit from exchanging goods and services between them, while everything else remains the same.
If nothing else, because rich and poor people value things differently (and even among each group, at any point in time each person also values things differently to a great degree).
But what does this even mean? The buying power of the dollar (or its “equivalent”) where those people live can be much higher than in the US. (Unless you mean to compare with living on that much per day in the US.)
Add a bit more income and suddenly people can afford bikes and books if they save up, that is the lowest point necessary for people to start to pull themselves up and improve their society which is why it is so important to get as many people as possible to at least that level.