This paper addresses the cluster containment control problem for a swarm of linear unmanned systems operating over a directed communication graph and subject to external disturbances, formulating it as a graphical differential game. Each agent independently computes a distributed optimal control strategy using only local information, ensuring both cluster containment and Nash equilibrium behavior within the game framework, while also maintaining robustness to external disturbances. The closed-loop system is proven to be asymptotically stable, and the existence of a Nash-minmax solution for each agent is established. To implement the control strategy without requiring a model of the system dynamics, a model-free, data-driven reinforcement learning algorithm is proposed for the online computation of distributed Nash-minmax control policies, accompanied by convergence guarantees. The effectiveness of the proposed framework is demonstrated through simulations involving swarms of unmanned aerial vehicles and unmanned ground vehicles.