how exactly is energy extracted from such a system?
In the ball-car collision the electromagnetic forces are the ones responsible for changing the direction of the ball. But in the binary system, it is gravity. In particular as the shuttle enters orbit around the "incoming" star, the star's gravity will pull it forward mostly when it completed half orbit.
I hope I make sense.
Overall, such a joy to read this paper. With basic physics it makes you dream of sci-fi...
EDIT: typos
https://en.wikipedia.org/wiki/Gravity_assist
there is nothing speculative about it