It looks like this model has the same animation bug that has affected a few other models in the past. I tested it with the branch https://github.com/AnalyticalGraphicsInc/cesium/pull/5740 and the animation worked correctly. That PR should get merged before the next release.
I think the normals are correct but the winding order of the triangles is clockwise instead of counterclockwise, which means the front faces are being culled instead of the back faces. As a quick fix, edit the material in the gltf by setting doubleSided to true. It’s possible the other engines are doing this by default. Also, I tried both the .gltf and .glb in Cesium and they loaded fine, nearly instantaneous for me. I’m not sure what would cause the slowdown for you.
It can only be done in the .gltf, but you should be able to convert it back to a .glb pretty easily (for example, here https://sbtron.github.io/makeglb/)