With the advent of 5G, supporting high-quality game streaming applications on edge devices has become a reality. This is evidenced by a recent surge in cloud gaming applications on mobile devices. In contrast to video streaming applications, interactive games require much more compute power for supporting improved rendering (such as 4K streaming) with the stipulated frames-per second (FPS) constraints. This in turn consumes more battery power in a power-constrained mobile device. Thus, the state-of-the-art gaming applications suffer from lower video quality (QoS) and/or energy efficiency. While there has been a plethora of recent works on optimizing game streaming applications, to our knowledge, there is no study that systematically investigates the <QoS, Energy> design pairs on the end-to-end game streaming pipeline across the cloud, network, and edge devices to understand the individual contributions of the different stages of the pipeline for improving the overall QoS and energy efficiency. In this context, this paper presents a comprehensive performance and power analysis of the entire game streaming pipeline consisting of the server/cloud side, network, and edge. Through extensive measurements with a high-end workstation mimicking the cloud end, an open-source platform (Moonlight-GameStreaming) emulating the edge device/mobile platform, and two network settings (WiFi and 5G) we conduct a detailed measurement-based study with seven representative games with different characteristics. We characterize the performance in terms of frame latency, QoS, bitrate, and energy consumption for different stages of the gaming pipeline. Our study shows that the rendering stage and the encoding stage at the cloud end are the bottlenecks to support 4K streaming. While 5G is certainly more suitable for supporting enhanced video quality with 4K streaming, it is more expensive in terms of power consumption compared to WiFi. Further, fluctuations in 5G network quality can lead to huge frame drops thus affecting QoS, which needs to be addressed by a coordinated design between the edge device and the server. Finally, the network interface and the decoder units in a mobile platform need more energy-efficient design to support high quality games at a lower cost. These observations should help in designing more cost-effective future cloud gaming platforms.