As it stands, it's the US and China (despite the Trump administration's distaste for science) that seem set on becoming the world's AI superpowers. Sorry, Russia, but I doubt it will have top-tier potential due to its relatively tiny, resource-based economy, unless Russian research progresses by leaps and bounds.
I fear we are ceding too much ground to China in terms of R&D, not only with AI but supercomputing as well
(which I guess go hand-in-hand). Personally, I believe any kind of superintelligent AI is going to require specialized processors that are suited to learning, but overall the entire area is particularly vulnerable to IP theft. Russia may suffer from brain drain and not have the resources to lead the charge for AI itself, but it could definitely wait for someone to get close and then steal it. Ditto for China - a country who has made stealing technology a staple of its national advancement strategy.
But to what you said - I do agree, Putin is right. AI is only going to be more and more important, and it's really something America can't afford to fall behind in. At its core, this is a race to develop a form of computer intelligence that can solve our problems with record speed and efficiency, and it goes without saying that all the major world powers include the problem of how they can achieve superpower status and stay there.