What did German Arciniegas Angueyra mean by "After the advent of Christianity no other event has brought about a radical change in European thinking as the actual discovery of America"?
German Arciniegas Angueyra meant that the discovery of America, by Europeans, meant that Europe could no longer ignore the fact that there was a significant land mass with native people (and eventually others) that would in essence demand their attention. Europe could no longer believe itself the pre-eminent configuration of nations, or if they did, it would not be forever. A new nation would eventually rise that would rival Europe economically and militarily.
With the discovery of America, Europeans would have to think differently, and extend and expend their resources differently, whether they wanted to or not. A perfect example of this is the French and British sending people and physical resources to the New World. Spain did also. Wars would be fought on New World land. America also became the land of opportunity, as did Canada. This resulted in an influx of settlers from Europe to the New World.
Therefore, Europe had to change its international outlook and consider a new entity. America would be a competitor as well as an ally in the ensuing years. The sometimes volatile, often friendly, and always unique relationship between Europe and America exists to this day. This relationship is often at the whim of the respective leaders of the concerned nations.