Anisotropic shear relaxation is an interesting but rarely discussed issue in polymer dynamics under confinement. According to the earlier study of bead spring simulations for an unentangled polymer melt confined between two flat plates, the shear relaxation modulus taken perpendicular to the interface is accelerated by decreasing the distance between plates, whereas the parallel component is unchanged [Abberton et al., Macromolecules, 48, 7631, 2015]. This study observed similar anisotropic shear relaxation for entangled polymer melts under confinement in multi-chain slip-link simulations (primitive chain network simulations) for shear relaxation moduli obtained by the Green-Kubo formula. The analysis demonstrated that the accelerated relaxation in the perpendicular component reflects the Rouse-type constraint release dynamics, for which the coarsening is upper-limited by the geometry. This result suggests a novel mechanism for anisotropic shear relaxation different from the modified chain statistics under confinement considered for unentangled systems unless the obtained relaxation moduli reflect artifacts from the use of the Green-Kubo formula under confinement.