A WAY over-engineered solution to a first-world problem. Saw an article saying cats need to play with their food to feel fulfilled, and said, "Hold my beer."
Pour food into the top funnel, and it gets spread out into the puzzle level. The cat can see the food and bat it around, but can't get it out unless it pushes the food into the holes in the central tube. The food then falls down a level, either onto the plate, or onto the next lower puzzle level if it exists.
This model takes a lot of plastic and a lot of time to print. Before you start, print Screw_Test.stl to make sure your settings will make functioning screw joints. If it doesn't work, don't bother with the other pieces.
Print 1 "plate", 1 "lid", and as many "puzzle" parts as you want (too many, and it will likely topple). The pieces screw into each other, but you might still want a spot of glue.
Supports are only necessary on the small rims that are parallel to the ground and in the windows, so set your supports to 80 degrees if using Cura.
Some say that printed PLA is not safe to eat off of. If you are concerned, either look for food-safe PLA or avoid this project.
Also, you are responsible for the safety of your pet! Make sure its head does not fit in the windows. Make sure you sand any sharp edges! Watch out for breakage. I refuse any responsibility for whatever happens to your pet from your use of this model. If you do not agree to take 100% responsibility, do not use this model!