What Zakaria is saying in this essay is that we are wrong when we worry about the United States falling behind in the competition for power (economic, social and political). He says that we are not falling behind. Instead, he says, the rest of the world is catching up. And this is, he says, a good thing.
We have worked hard to create a world with free societies where people could have economic opportunity. Now these societies are starting to exist all over the place. We should be happy.
He says that the rise of these places can be really good for the US because we are an open and flexible society. Immigrants can come here and help our economy (as in the example of engineers). We can sell our knowledge and innovative abilities to these rising countries.
In other words, this is not a zero sum game. The rise of the rest will help us too.