This paper proposes a framework that simultaneously integrates unmanned aerial vehicle (UAV) mobility, backscatter communication (BackCom), and rate-splitting multiple access (RSMA) to enhance task offloading. In the proposed system, the UAV acts as a mobile airborne base station assisted with a mobile-edge computing (MEC) server, which not only provides carrier signals that can control backscatter edge device (BEDs) but also supports efficient task offloading via RSMA. To evaluate the offloading performance of the system, we derive a closed-form expression of the successful computation probability (SCP) under Nakagami-m fading. Simulation results demonstrate that the proposed scheme significantly outperforms the benchmark schemes based on conventional nonorthogonal multiple access (NOMA). In addition, this work establishes the fundamental integration of RSMA with symbiotic UAV-BackCom systems, paving the way for future sustainable and high-capacity Internet of Things (IoT) networks.