Integrating digital twins (DTs) and multi-access edge computing (MEC) is a promising technology that realizes edge intelligence in 6G, which has been recognized as the key enabler for Industrial Internet of Things (IIoT). In this paper, we explore a DT-assisted MEC system for the IIoT scenario where a DT server is created as a digital counterpart of the MEC server, via estimating the computation state of the MEC server within the DT modelling cycle. To achieve energy and spectrally efficient offloading, we consider that IIoT devices communicate with industrial gateways (IGWs) through a non-orthogonal multiple access (NOMA) protocol. Each IIoT device has an industrial computation task that can be executed locally or fully offloaded to IGW. We aim to minimize the total task completion delay of all IIoT devices by jointly optimizing the IGW’s subchannel assignment as well as the computation capacity allocation, edge association, and transmit power control of IIoT device. The resulting problem is shown to be a mixed integer non-convex optimization problem, which is NP-hard and challenging to solve. We decompose the original problem into four solvable sub-problems, and then propose an overall alternating optimization algorithm to solve the sub-problems iteratively until convergence. Validated via simulations, the proposed scheme shows superiority to the benchmarks in reducing the total task completion delay and increasing the percentage of offloading IIoT devices.