Earlier quoted context omitted.
The poor are moving up, the middle class are moving toward the poor (they will meet at some point), and the rich continue to get richer in the process. So yes, inequality is technically decreasing between the poor and middle class, but the end result will be the middle class being non-existent. It might be better for someone from a poor country, but not that good for someone from the US.
I don't believe that it is the divine right of the middle class of one country to live better lives than other people, simply because of location. Besides, globalisation will overall increase the total wealth of the poor + middleclass combined.
It won't really increase the overall wealth of the middle class. It will pull wealth away from the middle class to pay the poor at a cheaper rate. This is what's happening right now and why people in the tech industry are so upset by it. It's a form of global wealth redistribution.
I also don't think the middle class has any divine right. They just need to start preparing for job loss and overseas competition.