It would be a misreading to think that example implies a more limited scope. The passage as a whole is pretty clear why they are they so broad: in order to avoid circumvention. I can understand why - it seems to be both a necessary yet unacceptable way to write laws!

The passage continues:

"To prevent the circumvention of this Regulation and to ensure an effective protection of natural persons located in the Union, this Regulation should also apply to providers and users of AI systems that are established in a third country, to the extent the output produced by those systems is used in the Union."

An AI would come under this regulation even it's just the outputs that are used in the EU. Interesting to think about what that could lead to.