I'm thinking of nation states, but I fear you have a very limited view of how power is created and yielded.

AI doesn't have to be used offensively to give a nation power. The machines can already design new software at the drop of the hat, it will at some point become capable of designing new consumer and industrial products. Putting a tireless intelligence at the task of looking for new optimizations in your industrial processes and factories will eventually give you economic dominance, one way or another.

Offensive uses don't need to be as extreme as you imagine them. We're already starting to see the effects of having meticulous automated hackers. Instead of a blitzkrieg, imagine your foes suffer from a constant stream of industrial accidents, unfortunate events and information leaks that can never quite be traced to your nation.

Finally, political power itself doesn't need to come from people acting in concert. There's always been wheeling, dealing, intrigue and bureaucracy. Once AI is sufficiently versed in legal matters, it'd allow political interest groups to overwhelm governments and private enterprises with objections and appeals, paralyzing their ability to carry out their agenda until they make concessions.

The possibilities of using intelligence for acquiring more power are literally endless..