He really shouldn't be using the Material Colour property... a reason why AppGameKit is likely not reading such, is because without an assigned texture the assumption is that it's a "Blank" Material.
Materials Colours are generally speaking "Place Holders" or "Colour Coding" for Development Purposes; it's a left over feature (and in FBX for Compatibility Purposes) prior to the advent of Group, Layer and Association Colours.
Like you'd use it to indicate Static Vs. Dynamic, IK Vs. HK, Mesh LOD, Interactive Vs. Non-Interactive... like you're not supposed to be using Material Colours.
As noted it's only there for Legacy Purposes.
The reason it works in FBX Viewer (Autodesk) and 3D Viewer (Microsoft)… is because they're designed to display the entire scene.
AGK also don't import Cameras, Lights, Helpers, Locators, etc. would you expect it to?
His choice is either using Vertex Colours … or a Texture / Shader Material.
That FBX doesn't automatically import Textures., that to me seems like lazy implementation.