Good read and useful knowledge given my current interest in the evolution of warfare from "old world" (pre-WW1) to "new world". While I'm not sure any lone element can take the credit for something as complex as the rise of an international empire, certainly guns made a huge difference.
Somewhat of a deviation here but one thing I think people underestimate sometimes is how much disease did the job for colonists, particularly regarding the Americas, and in the case of the North American Natives, much of it occurred well before Europeans moved past their initial settlements. It made the difference between having hundreds of thousands of native forces compared to the rather small number of combatants the natives ever had the chance to field (in terms of a broad historical perspective).
Then again one can look at the Zulu massacres (who were an extremely competent fighting force and had perhaps greater military expertise and planning than the settlers/colonists), which were a pretty stark example of what a small group of guys with machine guns can do against a very large group of foes who lacked firearms.
Of course, firearms also found their way into the hands of the native americans quite a bit more, and so had their populations not been so devastated by disease then I think our maps would look a whole lot different.
