This paper addresses the co-design problem of adaptive control for networked wind turbine systems that track the desired rotor speed while efficiently scheduling network communication. Unlike existing approaches, the proposed method integrates the control design and the communication considerations, ensuring asymptotic tracking of rotor speed under the generator torque saturation with significantly reduced communication load. Firstly, the communication scheme is developed using the dynamic event-triggering mechanism, which introduces the feedback signal in the sampling loop. Secondly, an auxiliary signal is designed to mitigate the negative effect of inevitable generator torque saturation, ensuring that the bounded controller asymptotically exits from saturation. Then, the adaptive torque controller is constructed with the compensation signals to guarantee asymptotic stability, and the measurement function for dynamic event-triggering is co-designed alongside the controller to regulate the sampling-induced error. Furthermore, the requirement for exact knowledge of the wind turbine systems is eliminated by utilizing an online approximator to learn the uncertain aerodynamics and parameters. Finally, it is theoretically proven that all the signals in the closed-loop system are bounded, and the rotor speed asymptotically tracks the reference rotor speed. The feasibility and advantages of the proposed method are demonstrated on the NREL 5-MW wind turbine using the high-fidelity OpenFAST simulation platform.