What is the Gentile system preparing for according to this teaching?
The Gentile system is preparing for its demise, which is the Second Coming of Christ. At that return, Christ will destroy the image beginning with its feet, destroying first the revived Roman Empire—the empire contemporary with that day, which still contains remains of the earlier empires.
Les explains that Western Europe is rising and will become the empire of the world, and that the whole Gentile system finally prepares for its demise at the Second Coming of Christ. Because the image is standing, the smashing begins with the feet, so Christ destroys first the empire contemporary with that day, the revived Roman Empire. That revived empire contains remains of the previous empires. Les notes that banking and business, or using money for usury, began with Babylon, and that Rome integrated the profitable Greek culture into its own empire.
Then was the iron, the clay, the brass, the silver, and the gold, broken to pieces together, and became like the chaff of the summer threshingfloors; and the wind carried them away, that no place was found for them: and the stone that smote the image became a great mountain, and filled the whole earth.