An RGB-D image encryption scheme is presented by combining a newly constructed 4D-ICTM hyperchaotic system with a reformulated quaternion gyrator transform (QGT). The proposed 4D-ICTM dynamics arise from the nonlinear combination of the ICMIC and Chebyshev maps with the tanh function and modulo operation. Their dynamical and statistical properties are examined using Lyapunov exponents, bifurcation diagrams, histograms, autocorrelation analysis, and correlation-dimension computation. To handle the heterogeneous RGB-D data, a dedicated preprocessing procedure converts the RGB channels and 16-bit depth data into four 8-bit components, which are represented jointly in the quaternion domain. The reformulated QGT is evaluated in terms of numerical consistency and computational cost using numerical error, SSIM, and execution-time measurements. The resulting encryption approach is further assessed through statistical analysis, adjacent-pixel correlation, floating-frequency analysis, graphic autocorrelation, and decryption-error evaluation. The experiments show resistance to the tested attack scenarios together with competitive computational performance. An encryption throughput of 43.32 Mbps is obtained at 406 cycles/byte, indicating the potential of the proposed scheme for RGB-D image encryption applications.