The autonomous discovery of bugs remains a significant challenge in modern software development. Compared to code generation, the complexity of dynamic runtime environments makes bug discovery considerably harder for large language models (LLMs). In this paper, we take game development as a representative domain and introduce the Game Benchmark for Quality Assurance (GBQA), a benchmark containing 30 games and 124 human-verified bugs across three difficulty levels, to evaluate whether LLMs can autonomously detect software bugs. The benchmark is constructed using a multi-agent system that develops games and injects bugs in a scalable manner, with human experts in the loop to ensure correctness. Moreover, we provide a baseline interactive agent equipped with a multi-round ReAct loop and a memory mechanism, enabling long-horizon exploration of game environments for bug detection across different LLMs. Extensive experiments on frontier LLMs demonstrate that autonomous bug discovery remains highly challenging: the best-performing model, Claude-4.6-Opus in thinking mode, identifies only 48.39% of the verified bugs. We believe GBQA provides an adequate testbed and evaluation criterion, and that further progress on it will help close the gap in autonomous software engineering.