I don't think that it will be "the solution", but it will help in curbing the trend. Why do I think so? An autonomous car does not come cheap. So will initially only be bought in relevant quantity in developed countries (e.g. Europe, America, Japan). However, quoting from your article: "Over 90% of all road fatalities occur in low and middle-income countries, which have less than half of the world's vehicles." The market penetration of autonomous cars will go much slower in those countries. It wouldn't surprise me if these countries will lag the developed countries by 10 to 20 years.
The articles I read say the dead toll was mainly due to high speed accidents on highways. Therefore, there would be a restriction that only autonomous cars will be allowed on high speed highways in order to reduce deaths.
The original source where the "1.3 million deaths & 20-50 million injured" comes from is a report by UN's World Health Organization, written in 2013. Since then is every website and organisation copying these numbers. Further study from USA data concluded that some 93% of the car accidents were due to "human error". This includes among others speeding, drunk driving, drowsiness, distraction, and other causes. With the increase of elderly drivers is also the number of accidents due to mistakes increasing (e.g. pressing the throttle instead of the brakes). Don't forget that in countries other than the USA it is often the "non-car driver" who gets killed when getting involved in a car accident (e.g. motor bike, bicycles, pedestrians). People seated in cars are often better protected for any impact due to a crash.
I just think it is possible that autonomous cars could possibly reduce those various accidents due to AI technology plus IR sensors for early detecting/avoiding any direct hitting/hurting human bodies. Perhaps we should not underestimate future technological advancement, like AlphaGo. Just 2 cents. " Road crashes cost USD $518 billion globally, costing individual countries from 1-2% of their annual GDP. "
Certainly, autonomous cars will contribute. But if their market penetration is low (e.g. market share of 10% or 20% of the cars on the road) their impact on reduction of casualties will be limited. The remaining 80%~90% of conventional cars will still continue to be involved in crashes.
In order for driverless cars to curb crashes they will have to be implemented everywhere and people shouldn't have access to actually taking control manually, but I am not sure how the general public will be convinced to give up such control.
Driver-less planes have been developed for long time, therefore general people don't need to learn flying planes anymore in the future. The future generation of people could be the same - not knowing how to drive cars. As the future cars cannot be controlled/overridden by human at all.