Unmanned aerial vehicle (UAV) base stations (BSs) can be a promising solution to provide connectivity and quality of service (QoS) guarantees during temporary events and after disasters. In this paper, we consider a scenario where UAV-BSs are serving large number of mobile users in a hot spot area (e.g., in a stadium). We introduce non-orthogonal multiple access (NOMA) transmission at UAV-BSs to serve more users simultaneously considering user distances as the available feedback for user ordering during NOMA formulation. With millimeter-wave (mmWave) transmission and multi-antenna techniques, we assume UAV-BS generates directional beams and multiple users are served simultaneously within the same beam. However, due to the limitations of physical vertical beamwidth of the UAV-BS beam, it may not be possible to cover the entire user region at UAV altitudes of practical relevance. During such situations, a beam scanning approach is proposed to maximize the achievable sum rates. We develop a comprehensive framework over which outage probabilities and respective sum rates are derived rigorously and we investigate the optimal operational altitude of UAV-BS to maximize the sum rates using our analytical framework. Our analysis shows that NOMA with distance feedback can provide better outage sum rates compared to orthogonal multiple access.