While Europe may need unification in order to stay relevant on a world stage, not all signs point to this being successful. It would be equally likely and possibly equally interesting to have them fall from the stage into obscurity and or infighting. Not that either result would really have anything to do with us.

America.... well, you could run it as still the top dog and have it be far from its founding ideas either in principle or practice.

You seem to have ruled out India entirely and give Russia too much credit.

Anyway before I get into everything a great way to shake up the power structure of the world would be with a good old world war. Well, two of them. World wars seem to come in two's if you count the Punic wars that were not just a single siege and conflicts between Greece and Persia. Sticking to a historical model would mean that an underdog wins the first war and starts to become a greater power and then they also win the second war, cementing their global dominance. Or you know, known world dominance in the earlier cases. And you could really do whatever you wanted with that as it would involve too many variables to reasonably account for.