In this paper, we propose a Slotted ALOHA (SA)-inspired solution for an indoor optical wireless communication (OWC)-based Internet of Things (IoT) system. Assuming that the OWC receiver exploits the capture effect, we are interested in the derivation of error probability of decoding a short-length data packet originating from a randomly selected OWC IoT transmitter. The presented OWC system analysis rests on the derivation of the signal-to-noise-and-interference-ratio (SINR) statistics and usage of finite block-length (FBL) information theory, from which relevant error probability and throughput is derived. Using the derived expressions, we obtain numerical results which are further utilized to characterize the trade-offs between the system performance and the OWC system setup parameters. The indoor OWC-based system geometry plays an important role in the system performance, thus the presented results can be used as a guideline for the system design to optimize the performance of the SA-based random access protocol.