We always assume the axial load is dissipated into the sheetpile or soldier pile wall then into the soil. The walers must be welded to the walls, particularly near the ends of the wales. A free-body diagram of the wale and load path would show that the end reactions pass must pass through the welds, then into the perpendicular walls, then into the soil. Obviously, the welds must be capable of resisting the reaction load, and the perpendicular walls are treated as if they are diaphragms. The diaphragms must be (and usually are)stiff enough to tranfer the load.
In a one-story building subject to wind load, the wind load is transfered from the walls to the foundation at the bottom and to the roof at the top. The roof diapragm must be stiff enough to transfer the load to the moment resisting frame. AISC has a guide for determining the stiffeness of the roof. Using that guide you'll find that a sheetpile wall has plenty of stiffness to accept the "dissipated" load from the wale end reaction.