Heh, it kinda is, but the tamagotchi has a tendency to grow massive limbs and smash people and small animals into bits.
Here's the process of feeding your creature...
Shot 1: Use the teleport ability to catch a rabbit... Note the piles of coal from fireballed trees.
Shot 2: Once captured, he will appear in the food bar, press the "use" button to put him in the monster's lair...
Shot 3: Now once in the lair, you can bring your mouse over the rabbit to attract your creature towards it.
Shot 4: Delicious!
P.S. The bar you see in the top right of the screen that increases when the monster ate the rabbit is the hunger bar, once it reaches the limit your creature evolves.