Edge artificial intelligence (AI) is an emerging paradigm that leverages edge computing to pave the last-mile delivery of AI. To satisfy the increasing demand for high-performance computing and low latency of edge service, heterogeneous computing accelerators, especially Neural Processor Units (NPUs), are widely deployed on edge nodes. However, the edge AI heterogeneous computing system encounters the challenge of energy constraints. In this paper, we investigate the energy efficiency (EE) optimization problem in heterogeneous computing-assisted non-orthogonal multiple access mobile edge computing (NOMA-MEC) network model. Edge devices are configured with CPU-NPU heterogeneous computing processors to improve the AI task processing, and NOMA is applied to edge task offloading to enable massive connectivity. The system-centric energy efficiency maximization problem is studied. We formulate a system-centric energy efficiency maximization problem. To solve this problem, we decouple the original problem into two subproblems, i.e., the optimization problems of heterogeneous computing workload splitting and task offloading. A heuristic algorithm and binary search algorithm are proposed to optimize NOMA user pairing and task offloading delay, respectively. Furthermore, we propose a multi-objective alternative iterative algorithm to optimize system energy efficiency. Numerical results show that the proposed scheme can significantly improve the energy efficiency of heterogeneous computing-assisted NOMA-MEC networks compared to the existing baselines.