This paper explores the performance of wireless-powered-based short-packet communication systems in light of multiple interference sources. In which, a source node uses energy harvested from multiple power beacons to serve its destination, and data communication is executed using a finite blocklength scheme. To quantify the system performance, an approximation for the cumulative distribution function of the received signal-to-interference-plus-noise ratio at the destination is derived in a closed-form manner. This approximation helps in finding a closed-form expression for the average block error rate (BLER) performance, facilitating the understanding of the relationship between the number of transmitted information bits and packet length design as well as the impact of other system parameters. Monte Carlo simulations validate the mathematical model and show that the average BLER performance decreases with a higher data amount but improves with a larger number of packet lengths and time-splitting coefficients for information transmissions.