Achieving high spectral efficiency (SE) is of paramount importance for unmanned aerial vehicle (UAV)-aided wireless communication networks mainly due to the limited energy resources on board of a UAV. On the other hand, nonorthogonal multiple access (NOMA) is identified as an effective technology for enhancing SE. In this paper, we introduce NOMA transmission considering user distances as the available feedback, to UAVs serving as aerial base stations (BSs) at a large stadium potentially with several hundreds or thousands of mobile users. In particular, UAV-BS generates directional beams and multiple users each having a target rate based on their quality of service (QoS) requirements, are served simultaneously within the same beam employing NOMA transmission. User ordering for NOMA formulation is determined based on user distances and hence, users have to feedback only their distance information. We develop a comprehensive framework over which achievable outage probabilities and respective sum rates are derived rigorously for the distance feedback based NOMA strategy, which are verified through extensive simulations. Our analytical and simulation results show that NOMA with distance feedback can provide better sum rates compared to its orthogonal counterpart. Further, we identify optimal hovering altitudes for UAV-BS to maximize sum rates under different transmit power values.