A true mirror requires a cube map and the only place you see that ingame is on water. Appears to be hardcoded in the engine.
A true mirror requires rendering the scene twice: once with the camera "mirrored" over to the other side of the reflecting surface, looking "out" to create the reflected image, then a second time with that reflected image mapped onto the reflecting surface as a texture. There's no need for a cube map when the reflecting surface is flat, but it does require specific support from the engine's rendering code, to render the reflection and use it as a texture source for the final rendering pass. It'd be possible to use the same technique for a flat mirror, but the engine doesn't implement it for meshes, only for water.
A cube map is needed for reflections on non-flat surfaces, where an object reflects its full surroundings. Cube maps aren't tied to "real" reflections, though -- the fake reflection on that LPotD armor is a pre-rendered cube map of generic outdoor surroundings, stored in the textures BSA file as ishmaeltheforsaken said.
It's possible to do true reflections on a convex object like that armor, but it involves rendering the scene
seven times every frame, six to build the cube map plus one to render the object with the cube map applied. That's prohibitively expensive in terms of GPU throughput, so game engines don't do it.