Hybrid automatic repeat request (HARQ) is an essential technology that efficiently reduces the transmission error rate. However, for ultra-reliable low latency communications (URLLC) in the 5th generation mobile communication systems and beyond, the increase in latency due to retransmission must be minimized in HARQ. In this paper, we propose a highly-efficient low-latency HARQ method built on non-orthogonal multiple access (NOMA) for URLLC while minimizing the performance loss for coexisting services (use cases) such as enhanced mobile broadband (eMBB). The proposed method can be seen as an extension of the conventional link-level non-orthogonal HARQ to the system-level protocol. This mitigates the problems of the conventional link-level non-orthogonal HARQ, which are decoding error under poor channel conditions and an increase in transmission delay due to restrictions in retransmission timing. In the proposed method, delay-sensitive URLLC packets are preferentially multiplexed with best-effort eMBB packets in the same channel using superposition coding to reduce the transmission latency of the URLLC packet while alleviating the throughput loss in eMBB. This is achieved using a weighted channel-aware resource allocator (scheduler). The inter-packet interference multiplexed in the same channel is removed using a successive interference canceller (SIC) at the receiver. Furthermore, the transmission rates for the initial transmission and retransmission are controlled in an appropriate manner for each service in order to deal with decoding errors caused by error in transmission rate control originating from a time varying channel. We show that the proposed method significantly improves the overall performance of a system that simultaneously provides eMBB and URLLC services.