Cloud gaming, as one of the most promising live-streaming services, has garnered great attention by reducing client hardware requirements. However, it faces major challenges in maintaining high-quality user experience due to varying network conditions. From a network adaptation perspective, existing adaptive strategies can be categorized into adaptive bitrate (ABR)-based and adaptive frame rate (AFR)-based schemes. While ABR adapts well to bandwidth, it introduces redundant key frames, reducing video quality. AFR, on the other hand, avoids redundant key frames but has limited bandwidth adaptability. To tackle network variation and ensure high-quality experiences in cloud gaming, we propose nHAS, a hybrid adaptive live streaming scheduling system with neural compensation. nHAS integrates a deep reinforcement learning (DRL)-guided hybrid adaptive algorithm that dynamically optimizes bitrate and adjusts the resolution and frame rate to minimize redundant data. Additionally, to compensate for the impact of low frame rate and low resolution on video quality, we design a lightweight neural-compensated module tailored to the real-time and content-homogeneity characteristics of cloud gaming. Extensive evaluations demonstrate that nHAS increases video multi-method assessment fusion (VMAF) score and quality of experience (QoE) by 1.97 and 12.4% over the baseline.