What happens in America, influences significantly the rest of the world. Yes. But it's almost orthogonal to the question of how to win the battle within America.

If the hypothesis "if you play nice, you are more likely to win (because people will enjoy joining your side), and if you play dirty, you are more likely to lose (because neutral people will hate you, and you will also have a lot of internal fighting)" is true -- which is the thing being debated -- then the fact that the outcome in America will strongly influence the rest of the world, just makes it more important to play nice in America.

More meta: If you believe some strategy is the winning strategy, increasing stakes should make you follow the strategy more carefully, not abandon it.