This study investigates the neural-network (NN)-based adaptive decentralised controller design issue for a class of large-scale non-linear non-strict-feedback interconnected systems with time-varying asymmetric output constraints and deadzone inputs. The existences of the non-strict-feedback structure, time-varying asymmetric output constraints, and dead-zone inputs lead to the construction of the controller of each subsystem is very difficult. By applying the inherent property of Gaussian functions employed in radical basis function NNs, the non-strict-feedback structure is skillfully handled, and the adaptive backstepping method is used to construct the desired controllers of all subsystems. Furthermore, Lyapunov stability analysis shows that all the signals of the closed-loop system are ultimately bounded, and each subsystem output can converge to an arbitrarily small and predefined time-varying range with the corresponding constraint is always satisfied by employing a barrier Lyapunov function. Finally, simulation results based on a practical example prove the effectiveness of the proposed design strategy.