When I play this game, I really feel like a cat stalking its prey, so you nailed the core mechanic.
They live in your garden, and their life is precious to you. Whenever you bring them home, you get praised and cuddled. They are, in a sense, a currency, their life for your pleasure.
If you want to play the original jam entry, please download the file named accordingly. The browser version is not significantly different right now (like, z-buffer fixes), but this can change in the future.