Did President Obama commit the zero-sum fallacy?

The Economist thinks that the President made a serious mistake when he said his goal was winning the economic "war" with China, as if their prosperity is going to somehow make us worse off.

People who live outside of America are people just like Americans, and we should all rejoice in their rising prosperity, the more so when it occurs through additions to the stock of human knowledge that will benefit people everywhere. If an American president can't communicate that simple idea to his citizenry, out of fear that he'll be drummed out of office on a wave of nationalistic outrage, then he doesn't deserve to be president and his country doesn't deserve to win a damned thing, least of all the right to call itself "exceptional", a beacon of hope and freedom. A zero-sum world is a world without hope, and if Mr Obama is convinced that's what we're in then I don't see much need for him to stick around.