What does Zakaria see as the major strengths of the U.S. as a global power in the 21st Century?
I think that there are a couple of ways to answer this question.
First, you could go with the message of the following quote from Zakaria:
At the military and political level, we still live in a unipolar world. But along every other dimension—industrial, financial, social, cultural—the distribution of power is shifting, moving away from American dominance
If you look at it this way, Zakaria is saying that our strengths are political and military. He is saying that the US is the only country that has any sort of a claim to being a superpower. Only we can project force anywhere in the world. Only we are a major player in every important political decision (who cares what China and Russia think about the Israel-Palestinian conflict, for example).
The other way to look at this is seen in this quote:
More broadly, this is America's great—and potentially insurmountable—strength. It remains the most open, flexible society in the world, able to absorb other people, cultures, ideas, goods, and services.
Here, Zakaria is saying that the US is and will remain great because of the openness of our society. Unlike Japan or China, for example, we welcome immigrants no matter where they are from. This openness keeps us flexible and "young." Because of this, we will be able to adjust to the new reality as other countries become prosperous and somewhat more powerful.