The Countries most at risk for Human extinction caused by Artificial Intelligence are China, Russia and the U.S.

The main Reason China and Russia are at risk from AI human extinction of everyone in their countries is pretty simple: The general lack of oversight and checks and balances.

The main reason the U.S. is at risk is people who think a lot like Trump who are paranoid and more likely to be armed to the teeth because of their paranoia to begin with.

However, the victims of Artificial intelligence will be "All Life on Earth".

How this will unfold is anyone's guess at this point? However, AI Death from the skies from Drones that are Autonomous is my best guess starting around 2050 to 2070 to where only 1 billion people or less are still alive by 2099 and most of them live underground without any cell phones with GPS to target them from Drones that are War Drones in the Sky that can loiter waiting for individual people that they want to target with missiles or hand grenades for 24 hours at present but by then they might stay up there a week or more using helium or hydrogen balloons to stay aloft longer air times. 

And I think the civilian populations in China and Russia or even North Korea will be the first to be completely driven extinct by AI powered Autonomous drones. No one will be able to come out from under the ground when these things are aloft around the world. Because they will wait as long as they have to day or night and since these things have night vision and radar there will be no way to escape them above ground for any living thing.

Also, they could be the size of a B-52 Bomber or as small as a fly and be lethal to mankind in various ways. Imagine 1 million artificial flies taking out whole countries with diseases or small lasers. And they wouldn't just take out humans they likely would take out all wildlife too.