This paper investigates the zero-sum differential game problem for a class of uncertain nonlinear pure-feedback systems with output constraints and unknown external disturbances. A barrier Lyapunov function is introduced to tackle the output constraints. By constructing an affine variable at each dynamic surface control design step rather than utilising the mean-value theorem, the tracking control problem for pure-feedback systems can be transformed into an equivalent zero-sum differential game problem for affine systems. Then, the solution of associated Hamilton-Jacobi-Isaacs equation can be obtained online by using the adaptive dynamic programming technique. Finally, the whole control scheme that is composed of a feedforward dynamic surface controller and a feedback differential game control strategy guarantees the stability of the closed-loop system, and the tracking error is remained in a bounded compact set. The simulation results demonstrate the effectiveness of the proposed control scheme.