With the emergence of fluid antenna (FA) in wireless communications, the capability to dynamically adjust port positions offers substantial benefits in spatial diversity and spectrum efficiency, which are particularly valuable for mobile edge computing (MEC) systems. Therefore, we propose an FA-assisted MEC offloading framework to minimize system delay. This framework faces two severe challenges, which are the complexity of channel estimation due to dynamic port configuration and the inherent non-convexity of the joint optimization problem. Firstly, we propose Information Bottleneck Metric-enhanced Channel Compressed Sensing (IBM-CCS), which advances FA channel estimation by integrating information relevance into the sensing process and capturing key features of FA channels effectively. Secondly, to address the non-convex and high-dimensional optimization problem in FA-assisted MEC systems, which includes FA port selection, beamforming, power control, and resource allocation, we propose a game theory-assisted Hierarchical Twin-Dueling Multi-agent Algorithm (HiTDMA) based offloading scheme, where the hierarchical structure effectively decouples and coordinates the optimization tasks between the user side and the base station side. Crucially, the game theory effectively reduces the dimensionality of power control variables, allowing deep reinforcement learning (DRL) agents to achieve improved optimization efficiency. Numerical results confirm that the proposed scheme significantly reduces system delay and enhances offloading performance, outperforming benchmarks. Additionally, the IBM-CCS channel estimation demonstrates superior accuracy and robustness under varying port densities, contributing to efficient communication under imperfect CSI.