Are textures also stored when exporting an asset to another Game Engine?

Hi there, if I want to export a Blender asset to, for example, Cryengine or Unreal Engine, how do I export so that the textures are also stored? I know that .OBJ files only store object data, so how do you import the texture data too so that the imported asset is fully textures with bump maps, normal maps, disp maps, etc?

.obj outputs the directory to the texture in the material (.mtl if selected by export) file. As long the importing software reads the file and the textures are still in the same directory it should work.
If are the textures packed into the file you can export it with File–>External Data–>Unapck All Into Files > Use files in current directory. This will also automatically converts all links to the relative textures folder. Then you can export an .obj, .fbx or .dae

Does not belong to Blender Game Engine. It belongs to Blender Export.