Although it doesn't look like it, my guess is the game uses some kind of lightmap (maybe a cubemap) for lighting the box (or at least for the specular), and the lightmap is rendered from the scene, but with a delay (less often than the main scene is rendered), so as it doesn't consume too many resources? But the lightmap from the environment is also blended with the old lightmap in small amounts, so that it doesn't transition abruptly from dark to light. That does seem like a weird way to do lighting, though. Note that the red and green light from the cauldron-thingy is not real light - it's just a polygon with a texture that looks like a point light, so it doesn't affect the lightmap of the box when the box is dipped in it.
I think developers often implement stuff like this in games that are supposed to run on older hardware, or consoles like the Xbox, which can't do deferred lighting for some reason... Or for mobile platforms, like the iOS .
Edited by tonemgub, 29 August 2014 - 01:26 AM.