The spectral efficiency of sixth-generation (6G) wireless networks is anticipated to experience large improvements through the implementation of non-orthogonal multiple access (NOMA) technology. The integration of short-packet communications (SPC) into NOMA networks enables low-latency operation and high spectral efficiency. The present study investigates the performance of multiple users in a NOMA downlink SPC system operating over an α − κ − µ shadowed fading channel. Precise and asymptotic closed-form approximations for the average block error rate (BLER), reliability, throughput, goodput, and overall BLER were derived using approximate Gaussian-Chebyshev quadrature. The analytical results were validated through numerical simulations, providing insights into the impact of fading parameters on system performance. The study’s findings indicate that the proposed downlink NOMA SPC system is highly suitable for ultra-reliable and low-latency communications (URLLC), achieving reliability levels of 99.99% for multiple users. The study also determined the optimal transmission bit rate required to maximize throughput and goodput while minimizing the BLER. The proposed downlink NOMA SPC system operating with an α − κ − µ shadowed fading channel demonstrates high potential for improving Internet of Things (IoT) network performance over conventional downlink orthogonal multiple access (OMA) approaches. Most of the analysis adopts perfect successive interference cancellation (pSIC) and perfect channel state information (pCSI) as theoretical benchmarks, while additional results explicitly quantify the performance degradation caused by residual interference and channel estimation errors (CEE). The results reveal that imperfect SIC (ipSIC) dominates the BLER floor at high signal-to-noise ratio (SNR), whereas imperfect CSI (ipCSI) primarily affects the moderate-SNR regime, highlighting distinct impairment-driven performance bottlenecks. Therefore, we have extended the study by including two additional scenarios: pCSI combined with ipSIC, and ipCSI combined with ipSIC. This extension allows us to compare the performance of these systems and clearly shows that the system with pSIC and pCSI achieves the best performance. Finally, the results were validated with Monte Carlo simulations.