This study investigates a novel resource allocation framework for a multi-user multiple-input multiple-output (MU-MIMO) downlink system that employs reconfigurable intelligent surfaces (RIS) within a rate-splitting multiple access (RSMA) scheme, specifically for ultra-reliable low-latency communication (URLLC). We aim to minimize the overall transmit power at the base-station while guaranteeing the rate quality of service of the downlink users in severely obstructed dead zones, where direct links between the base station (BS) and users are unavailable, with RIS serving as a relay to facilitate communication. To achieve this, we formulate a transmit power minimization problem that involves the joint design of active beamforming at the BS and passive beamforming at the RIS under given rate and URLLC requirements. Given the non-convex nature of the original problem, we propose an alternating optimization and successive convex approximation framework to solve it. Our proposed solution demonstrates rapid convergence within a few iterations, as validated by numerical simulations. The proposed RSMA scheme for the ARIS-aided downlink URLLC system outperforms conventional multiple access schemes in terms of power requirements.