Comparative advantage is undermined if the factors of production can relocate to wherever they are most productive: in today's case, to a relatively few countries with abundant cheap labor. In this situation, there are no longer shared gains - some countries win and others lose.
This is absolutely false. Ricardian comparative advantage can exist within a country. It can exist with mobile factors of production.
They go on to say that
To call America's economic recovery "jobless" is inaccurate. Lots of new jobs are being created, just not in the United States.
This also is false. What David Ricardo developed was the first general equilibrium model in economics. Anyone who understands the principle of general equilibrium understands that one country cannot "lose" jobs to another country. An industry can lose jobs, but in general equilibrium there is full employment.
When there is not full employment, this is an issue of fiscal and monetary policy. It is not an issue of trade.