But, it wasn’t in the language of the people!
Actually, the New Testament of the DouayRheims Bible was published two decades before the KJV and the Old Testament a few years before the KJV. It has long been acknowledged that the translators of KJV used portion of the DouayRheims New Testament in certain places.
The D-R and KJV were both translated by learned men, who had been educated in similar fashions, so it is not unusual that there are plenty of similarities among the two translations. Additionally, it's worth noting that when Bishop Challoner revised the D-R (the original had been mainly ignored by English-speaking Catholics) he relied heavily on the prose style of the KJV.
Though I am Catholic, I can certainly recognize that enormous impact that the King James Bible has had upon the world. Along with the works of Shakespeare, the KJV forms the basis for modern English; so, from the simply a linguistic point of view, the KJV certainly changed the world.
From a historical and political point of view, it gets a bit murkier. England's greatest era was certainly the three centuries which followed the KJV, much of the world was colonized by men who relied upon the KJV. However, though spreading Christianity was often the stated goal, the British were typically more motivated by power and profit. America is unique in that many Englishmen permanently moved to the colonies and our Founding Fathers descended from them and almost without exception these men viewed the KJV as the most important book ever written.