Looking at gameplay videos, I agree with phil_t.
The animations are not smooth, but are distinct steps. Most appear to be 3-6 frames, looped either end-to-end or ping-pong style.
Considering the cost of pixel art (it is far cheaper to capture 3D renders via script than to hand draw everything), I'm seconding the guess that they were 3D items rendered into sprites most likely. Sprites can be drawn with depth, in a 3D environment or a rendered environment using depth images or various types of rendering masks, which lets them move behind other objects.
It is also possible they are full 3D objects that used constrained directions and stepwise animation curves, but I think that is less likely.