In Multi-access Edge Computing (MEC) environments, Non-Orthogonal Multiple Access (NOMA) technology significantly improves spectrum efficiency and system access capacity through power-domain multiplexing. However, it also exposes edge servers to more complex resource contention and security risks. In particular, during Distributed Denial-of-Service (DDoS) attacks, conventional mitigation mechanisms often overlook users' quality of experience (QoE), which can lead to prolonged service degradation. To address this challenge, this paper investigates a QoE-guaranteed Edge DDoS Mitigation problem (QEDM) in NOMA-assisted MEC systems by jointly considering request scheduling and power allocation. First, the QEDM problem is modeled as a finite-strategy potential game, and a distributed game-theoretic algorithm, QEDMGame, is proposed. Then, through a multi-player best-response mechanism, the system converges to a Nash equilibrium, thereby achieving joint optimization of service rate and QoE. Next, experimental results on real-world base station deployment data demonstrate that QEDMGame outperforms several representative baseline methods. Additionally, theoretical analysis shows that QEDMGame exhibits strong convergence properties and performance guarantees.