The end if the inner wire is fixed on a non-moving part of the brake lever (farther up on the next set of levers, or just with the stop on your cross lever), while the moving part of the lever pushes the cable housing, thus having the same effect as any other lever, effectively pulling the wire through the cable. It's the same thing if the pull happens by pulling the wire or pushing the housing.
If you're still unclear on it, try using a brake lever that isn't attached to the handlebar. It works just as well, aside from not having good leverage, due to the design of the lever. But allowing it to float in space will show you that it doesn't matter which part of the brake lever actually moves, so long as the inner wire is pulled through the housing.