Why has China's integration into the global economy caused it to slow it's output?
Being integrated into the global economy means that country increases its trade openness and lifts restrictions on capital flows (you can look at this paper).
The article does not say that China's output slowed down. It says its rate of growth slowed down. Usually, a country that used to be closed and did not trade much before experiences a boost in the rate of economic growth. This is because trading allows the country to specialize in a good where the country has a comparative advantage. This boosts growth by a lot at the beginning but the effect eventually wears down as the country gets fully specialized and all low hanging fruit was already picked.