In this paper, an economic model is proposed for joint time resource allocation and energy trading between two service providers, i.e., IoT service provider (ISP) and energy service provider (ESP), in a heterogeneous IoT wireless-powered communication network. In particular, IoT devices (with various communication types and energy constraints) are assumed to belong the ISP who collects sensing data from IoT devices for its services. Meanwhile, the ESP utilizes a power beacon to provide energy services for the ISP. A Stackelberg game model is formulated to jointly maximize the revenue of both the ISP and ESP (i.e., network throughput and energy efficiency) through investigating the energy interaction between them. Specially, the ISP leads the game by requesting an optimal energy price and service time that maximize its revenue to the ESP. Following the requested deal from the ISP, the ESP supplies an optimized transmission power which satisfies the energy demand of the ISP while maximizes its utility. To obtain the Stackelberg Equilibrium, we first derive a closed-form solution for the ESP. Then two relaxed schemes (i.e., partial or joint energy price and service time adjustments) based on block coordinate descent (BCD) and convex-concave procedure (CCCP) techniques are proposed to solve the non-convex optimization problem for the ISP. Due to the selfish behavior of both players, we investigate the inefficiency of the proposed approach by proposing two baseline scenarios, i.e., non-negotiated energy trading and social welfare scenarios, and the Price of Anarchy (PoA). Finally, numerical results reveal that our approach can achieve significant improvements in revenues of both providers compared with conventional transmission methods, e.g., bistatic backscatter, and harvest-then-transmit communication methods.