In my post on "The Ballad of Lost C'Mell," I argue--well, more like assert without argument--that Cordwainer Smith invents the sexy cat-girl trope and subverts it by pointing out how C'Mell status as a sexy cat-girl is intertwined with her status as a slave/underperson. But when you read "The Game of Rat and Dragon," you might lean towards the interpretation that Cordwainer Smith really liked cats.
The plot here is practically non-existent, since the only things that happen are that (1) a bunch of human telepaths get ready for a space flight with their cat-derived partners, (2) the space flight is attacked by the mysterious anti-life dragons, and (3) the main human recuperates in a hospital and feels more love for his cat-derived partner than for the human nurse. If that's too much plot for a haiku, it's not too much for a sonnet.
In fact, most of the story is setting description, with a sideline in character description that further does work as setting. So we learn about the telepaths and their pin-sets (amplifiers) and the cat-derived partners who see the space monsters as rats and attack by launching light bombs. If there's a lesson here for aspiring sf writers, I would say that you shouldn't be afraid of making the science weird and metaphorical. I mean, the "dragons" here could pretty easily fit in with some trans-dimensional Cthulhoid horror and the idea of driving off monster with light has a childish simplicity that never seems silly when you're reading this story. (Afterwards, however, you might wonder if hiding under a blanket would be equally effective in driving off the dragons.)
As usual, Cordwainer Smith makes some connections in these stories (the plano-forming ships are piloted by scanners and that sort of travel makes the Instrumentality possible); and as usual, there are many nice little details, like the fact that the cats don't think in words and are disappointed when the "rats" they kill disappear.
But that all gets us to the weird part of this. There's nothing wrong with forbidden love stories. I'm not even sure there's anything wrong with love that's forbidden because of species-difference. But as another story where a man loves a cat-creature, I think we're within our rights to ask Cordwainer Smith, "why cats?"