Being wonderfully weird, capricious and regal, cats are easy to adore (even if it's just the brain parasites). Inexplicably compelling, they're also often ideal subjects for games.
My friend Soha (herself caretaker of an exceptionally elegant and social media-friendly cat called Garnet) has done an excellent roundup of five of her favorite cat-centric games over at Paste. I haven't tried all of these — in particular, The Cat Lady seems exciting:
The Cat Lady is not just about Susan’s depression and her relationship with the stray cats in her neighbourhood, but also about the friendship she forms with another emotionally lost woman named Mitzi and how it impacts their lives. There’s also a gruesome, awesome scene involving the cats helping Susan take out an enemy.
Shelter 2, which I had a troubled but worthwhile experience with here at Offworld, also makes the list, although a lynx and a housepet are certainly not alike. We'll allow it this once.
Soha previously wrote a great feature for Offworld about Twine games, healing and community.