Is the rest of the world really that dependent on emerging AI? I don’t think so. The US could cut off all foreign access to AI, nobody would notice.
It would definitely be a problem. A big one. Think of all the multi-national tech companies that have rolled out AI not only to their engineering teams but to their business teams now too. Suddenly your employees in the US can do more and do it quicker than your employees elsewhere. It would be a nightmare to try and manage.
Unless your country still use only analogue technology your country would definitely will be at the mercy of the country with AI superiority. Mythos showed how good it is at finding vulnerabilities and attack vectors for digital infrastructure. Imagine an attack on power grid which would result in a days long blackout in the middle of winter?