The two major players in the Monroe Doctrine (besides, you know, Monroe) are the United States and Europe. Yes, it's a little uneven, since Europe is a whole bunch of countries, but that's just how confident the U.S. was. Really, "Europe" primarily refers to Britain, France, and Spain, since they were the ones who had colonies in the Americas, but just in case, the message went out to everyone.

Europe is kind of the villain, but one of those Tywin Lannister-type villains who deserves your respect. Monroe refers to them often as the "European powers," including "His Imperial Majesty" (2) of Russia, and goes out of his way to mention that

[…] [t]he citizens of the United States cherish sentiments the most friendly in favor of the liberty and happiness of their fellow-men on that side of the Atlantic. (8)

Monroe also mentions several times that the U.S. won't interfere with either European wars in Europe itself, or any remaining colonies in the Americas. Europe is an opponent…but not one to be trifled with.

Monroe uses the different political systems and American neutrality to emphasize how Europe is separate from the U.S. He comments on how "[t]he late events in Spain and Portugal shew [sic] that Europe is still unsettled" (18), and insists that their political system won't make anyone in the Americas happy:

It is impossible that the allied powers should extend their political system to any portion of either continent without endangering our peace and happiness. (23)

Europe is the (respectable) threat that inspired the Monroe Doctrine in the first place. All of Monroe's comments are about it or America's relationship to it, and he uses the region's recent power struggles and politics as reasons why all the Americas has to stay independent. European empires controlled a lot of the world at this time, and Monroe is trying to make sure the U.S. doesn't get sucked into their vortex.