****SPOILERS****
My interpretation is that Cat and Sam are twin sisters, so when Sam died, Cat tried to remove all identifying aspects of herself, since looking at herself was looking at Sam. Red could be a boyfriend, a friend, a neighbor, I'm not sure it matters. The cat in the game could either be just a representation of Cat herself, or maybe a pet that they had?
I would love to hear what your idea of the story was, if you could PM me. Storylines are my favorite things in gaming, and yours making me think as much as it did was why it got 4 starts. The ambiance was nice, and the simplicity let the player focus on the plot. It's 4 instead of 5 because I would've liked a longer game and something with more choices, where you maybe didn't snap out of it (I understand your time constraints and how much work goes into these, so it's not a complaint).