Downhole inclinometers are susceptible to interference from various factors during geomagnetic field measurements, including drill tool magnetization, the borehole environment, and external electromagnetic noise. This can lead to significant errors in the drill tool azimuth angle calculation. Existing multi-point analysis methods can compensate for magnetic interference to a certain extent. However, the compensated azimuth angle still exhibits significant nonlinear characteristics, making it difficult to meet the requirements of high-precision downhole measurements. Therefore, this article proposes a regularized extreme learning machine (RELM) error compensation method based on improved chaotic game optimization (ICGO). First, a multi-station analysis method is used to perform preliminary correction for magnetic interference. Subsequently, a CGO-RELM compensation model is formulated, which uses triaxial accelerometer and magnetometer data as input and outputs correction residuals. The model is compared with RELM models based on particle swarm optimization (PSO) and genetic algorithms (GA). To address the problems of insufficient population diversity and local extrema in the original CGO algorithm, three random seed mutation methods, including chaos, Gaussian, and wavelet, are introduced. A three-stage fusion strategy is proposed to improve global search capability and convergence efficiency. Experiments show that the proposed ICGO-RELM method significantly outperforms competing algorithms in both fitting performance and generalization accuracy. Compared with the traditional RELM model, the mean absolute error (MAE) and root mean square error (RMSE) of azimuth angles are reduced by 94.1% and 93.1%, respectively, and the coefficient of determination is increased to 0.999 4. These results demonstrate that this method significantly suppresses nonlinear errors, improving downhole azimuth angle solution accuracy and providing a reliable technical approach for trajectory control and measurement while drilling in complex downhole environments.