The Gateses don't account for inflation in their prediction. Income may be higher in the future, but so will be living costs. The standard of poverty will simply be shifted. Furthermore, I think it's hard to reasonably expect a world in which almost no people are poor without considering the changes in consumption that will have to occur first. Present consumption levels won't be sustainable with more countries consuming at the level of the US, for example, unless new food/energy production innovations are able to mitigate it. (To that end, I admit to wishing the level of consumption of many western countries would be reduced.)

An anecdotal piece about income levels:

Currently, I'm in southeast Asia, and have seen first-hand income disparity. The city in which I'm living has seen a drastic increase in hotels over the past decade (someone reported 32 were approved in 2013, but they did not provide evidence), and many large roads have a hotel (or two) under development somewhere along them. These hotels are pristine and obnoxious. Beyond these main roads, within the bowels of the city blocks with narrower, labyrinthine, and occasionally unpaved streets, houses are barely adequate. With the chickens and other animals running between these houses, you feel like you're in a rural village. This is not specific to the entire city, but that you see it in a not-very-poor neighbourhood reminds you that poverty exists just behind the walls of rich hotels.

Food is incredibly cheap, $1 if you want something affordable; the most expensive meal I've had was $3, although I'm sure you can find more expensive food. Cooking isn't very efficient and cheap here, so most of your lunch and dinner comes from stalls or restaurants. Clothing is uneven; a branded T-shirt is $4, good shirt $30, and discounted shorts $10. Housing is cheap unless you want western amenities; I have a comfortable apartment in a quiet alley, with all the furnishings, a balcony, free drinking water, free laundry service, and free cleaning service for $230 a month. Tech doesn't appear to be very different; Laptops are 50% cheaper, as was an OTG cable, and when it was first released the S3 was $500.

The designation of all this as "cheap", however, depends on perspective. When comparing it with a country where good meals cost $20, especially ones that are relatively bland in comparison with the food here, one may view living comfortably here as an easy thing to do, but that's only if you earn a western-level amount. Instead, a good income here will barely cover my rent, which, seen from a local perspective, is actually quite obscene. And the longer I've lived here, the more I've found paying $3 for ribs harder to stomach. Earnings are commensurate with living costs, so when I think about whether I want to live here permanently and earn money here instead of in Europe, I have to consider that what would be a good income here would make it hard for me to return to the west with much pocket change. (For that reason, a friend works in the UAE and visits his wife here only every few months.)

If income levels increase here, so will restaurant bills, electricity, and the price of a laptop. The cost of everything will be higher, and everyone will be left with the same (in relative terms) amount of money to spend. The people who beg for 10 cents today will start begging for $1. Everywhere I've gone, it's been the same story: there's a balance between what you earn and what you pay; the only difference is the bracket surrounding those two numbers.

To me, the issue here isn't of income, but of prosperity. For many people, earning 10% of what they would in the west for often harder work is not a problem, because it's enough to support their families. What breaks my heart is that I can't drink tap water, am weary about my health, the rivers and air are heavily polluted, education depends on the interest levels of jaded teachers, and earning that 10% carries with it a significant cost to the environment. I desperately want the people here to be able to view the price of lunch for their family as flippantly as I did, but what I think they want more is to be able to assure that their children will be able to recover from sickness at a reasonable cost (for free in a perfect world), get a good education and hopefully make it to university (which is expensive but more prestigious here than in the west), have clean water and enough food, fewer power outages, and after that, enough money to afford the trinkets every modern human wants to show off to their friends. I believe they will take all that before higher income in 20 years to afford the same amount of what they get now.

I don't know whether any of this adds any value to the discussion or has too many fallacies (I think there is some appeal to emotion), but hopefully it was worth reading. Full disclosure: many of the people with whom I've worked here are in conservation and political science; I likely have an environmental bias, as well as bias relating to corruption and gender/class equality.