The payload-carrying vehicles, captive spacecraft, are lifted as by grasping an upward moving rope, something like a San Francisco Cablecar "gripper" grips the ever-moving cable in the slot in the street between the tracks, smoothly dragging the cablecar up the steep hill.
In the case of KESTS, the "moving cable" is a high velocity circulating series of discontinuous electric motor armature segments, and the "gripper" connects via electromagnetic coupling, a kind of electrodynamic brake, loosly dragging against the fast upward moving armature mass streams, pulling / dragging the spacecraft upward.
More simply put, the upward-moving part of the armature mass streams loosly couple its momentum to the spacecraft via electromagnetic inductive drag, lifting the spacecraft along the KESTS from the ground up into high earth orbit.
KESTS to GEO's Lifting and Lowering Spacecraft