Just a little insight:

When you render out something, you render it out in different passes (beauty, specular, shadow, zDepth, etc.) and then you composite it in another program (like After Affects, Shake, etc.).

It could very well be that they just cut corners by not having to re-render the shadow passes, considering that it's such a short clip and no where near noticable in the game.

This doesn't mean SquareSoft were lazy or they forgot about it, the most likely case is they were strapped for time and/or it wasn't in the budget to re-render out one small and insignificant shadow pass.