But the US is by far not the only such case. By the same token, China, India, Russia, Germany, Britain, France, not to mention the supra- and pseudo-state of the EU itself, are all political powers that have a decisive influence on the world. Come to think of it, even small(er) size may not prevent states from influencing life for huge numbers of people beyond their borders.
But even that's not all. States (and the EU) are not the only large actors with a global impact. Corporations have, clearly, a similar impact, especially if they are large, if they have unique technologies that are in great demand (e.g., pharmaceutical molecules), if they are able to control important resources (from oil through gas and, increasingly, drinking water), or if they are able to influence people's ways of thinking without most of them even noticing, like the media, especially the commercial visual media, or (what is increasingly overlapping with the former), the entertainment industry.
I hate to say this: I have no idea how to fix these concentrations of power with no public supervision.