We aim to secure a large-scale device-to-device (D2D) network against adversaries. The D2D network underlays a downlink cellular network to reuse the cellular spectrum and is enabled for simultaneous wireless information and power transfer (SWIPT). In the D2D network, the transmitters communicate with the receivers, and the receivers extract information and energy from their received radio-frequency (RF) signals. In the meantime, the adversaries aim to detect the D2D transmission. The D2D network applies power control and leverages the cellular signal to achieve covert communication (i.e., hide the presence of transmissions) so as to defend against the adversaries. We model the interaction between the D2D network and adversaries by using a two-stage Stackelberg game. Therein, the adversaries are the followers minimizing their detection errors at the lower stage and the D2D network is the leader maximizing its network utility constrained by the communication covertness and power outage at the upper stage. Both power splitting (PS)-based and time switch (TS)-based SWIPT schemes are explored. We characterize the spatial configuration of the large-scale D2D network, adversaries, and cellular network by stochastic geometry. We analyze the adversary's detection error minimization problem and adopt the Rosenbrock method to solve it, where the obtained solution is the best response from the lower stage. Taking into account the best response from the lower stage, we develop a bi-level algorithm to solve the D2D network's constrained network utility maximization problem and obtain the Stackelberg equilibrium. We present numerical results to reveal interesting insights.