The GDPR purports to apply to any EU person, no matter where they are. That's one of the many problems with it.
However, it is already the case that the EU casts a wide net. blekko got a demand for info from the EU regarding Google's dominance of the search space in relation to mobile apps. Most of the questions were about opinions, not facts. After consulting with our lawyers, they said that the small amount of advertising income we had from the EU was enough that the EU could demand that we answer, but we could ignore the first one and see if they asked again more firmly.