The consideration of multimedia Quality of Experience (QoE) has largely been ignored in emerging Non-Orthogonal Multiple Access (NOMA) research. In order to address the wireless video transmission challenge in NOMA wireless networks, a QoE-optimized communication power allocation approach for downlink wireless video service is proposed in this paper. By jointly analyzing and exploring the power budget of the Base Station (BS), the physical channel constraint, and the video packet quality influence, we connect the QoE to the optimal NOMA power allocation to various video packets. In particular, an analytical QoE model is established by taking transmission rate, packet size, and video content quality into consideration. Then we prove the concavity of the QoE objective function, such that the QoE maximization problem can be solved by finding the optimal power allocation array for all User Equipments (UEs) in the system. An optimized power allocation algorithm is proposed in the spectrum- shared power domain NOMA system based on a light- weighted binary search scheme. Numerical simulation results demonstrate that comparing with the conventional Orthogonal Multiple Access (OMA) scheme, the proposed QoE-optimized power allocation method in spectrum-shared NOMA can drastically improve the system QoE performance regardless of the number of UEs in the service. Furthermore, the proposed method also provides desirable QoE when UEs have different video compression rate-distortion requirements.