There's nothing magical about geographic boundaries. If trade between countries destroys jobs, so does trade between states, counties, cities, and individuals.
Unions are smart enough to recognize that it doesn't matter where the competition comes from, as long as people can whatever they're making for a lower price - they're toast. Doesn't matter if it's across town or across the globe. Which is why they do everything they can to either prevent people from buying from someone else, or hamstring their competitors with enough penalties to neutralize any price advantage that their competitors have.
Yes, the failure of the union movement to grasp and act on the necessity of a true international in the context of global capitalism has been a monumental mistake.
But anyway, simply saying that "trade destroys jobs" as if all this were just an unfolding of God's everlasting plan overlooks the vast arsenal that a state or other kinds of communities have at their disposal to shape the terms of those relationships and to mitigate the impacts in ways that actually benefit citizens (given of course that their political and intellectual leadership isn't composed of the kind of frothing zealots that we've had for the last few decades). I think that's the point of the paper, yes?