Why does the rise of Europe mean the decline of American influence?
Western Europe's ascent corresponds to America's declining clout because European companies are buying up American companies, shifting influence and power toward Europe. The context portrays this as part of a broader Gentile system that will culminate in a revived Roman Empire, which Christ will destroy at His Second Coming.
Les teaches that listeners should watch Western Europe because it is coming up, up, up. He explains that European companies are buying up American companies, so America is losing its clout while Europe is gaining. He connects this to the prophetic picture: Western Europe will become the empire of the world, and the revived Roman Empire is the empire contemporary with Christ's Second Coming. In that image, the roller smashes the feet first, destroying the contemporary empire, which includes remains of previous empires.