This paper applies a novel two-layer optimizing control scheme to a kite-control benchmark problem. The upper layer is a recent real-time optimization algorithm, called Directional Modifier Adaptation, which represents a variation of the popular Modifier Adaptation algorithm. The lower layer consists of a path-following controller that can follow arbitrary paths. Application to a challenging benchmark scenario in simulation shows that this two-layer scheme is capable of substantially improving the performance of a complex system affected by significant stochastic disturbances, measurement noise and plant-model mismatch, while respecting operational constraints.