There are many uses for AI that governments are interested in. Deepfakes, cheaper and more subtle ways to influence public opinions on the internet (by being able to instantly deploy thousands or millions of fully automated bots that are able to express their “opinions” in a way that is indistinguishable from humans), accurate and automated analysis of public discourse on the large scale, etc. And if you have an edge over other countries then you are able to influence their public opinions and detect (and possible counteract) when they try to influence you.

AI is very good at analysing human-generated data, as well as generating data that looks human-created. Any entity that deals with (and desires to control) a large number of people (of which governments are prime examples) will find many uses for it.