I’m not a material expert but I already handled texture cubes and equirectangular videos on spheres and skybox but in this case would be much better to use a cubemap rather than an equirectangular and a cube mesh rather than skybox.
The process is similar to playing equirectangular videos on spheres, only difference is that you must create your own cube mesh(using external programs like maya,3dsmax,blender etc.) with normals flip and UV according to your cubemap 360 video. Below is the link to help you on how you can play a video file inside a level on a Static Mesh with the File Media Source asset, which i guess you already know from playing equirectangular videos on spheres.