As a promising paradigm to support wireless connections among massive devices, the Internet of things (IoT) is facing several challenges. Among them, the energy supply to IoT devices, the weak computation ability of IoT devices, and the stringent latency requirement of IoT applications are three major challenges, which can be tackled by radio frequency energy harvesting, mobile edge computing (MEC), and short packet communications (SPC), respectively. In this paper, we investigate resource allocation in MEC-enabled wireless powered IoT (WP-IoT) networks with SPC, and formulate the problem of optimizing the computation frequency, the packet length and the packet error rate, targeting maximizing the sum effective computation throughput. Since the problem is difficult to solve in general, we first simplify the problem by analyzing its properties, then design an efficient algorithm to obtain a suboptimal solution in an iterative manner based on the bisection method, the block coordinate descent method, the successive convex approximation method, and the majorization-minimization method. Simulation results confirm the effectiveness of the proposed algorithm. Particularly, it is shown that the proposed algorithm is of low complexity and achieves the performance close to that of the optimal exhaustive search, while also significantly outperforms other benchmark algorithms in existing literature.