While I agree with your argument in general, I'm not sure I understand this particular use case. There is an owner of this game who holds a key and decides when and how to mint new cats and generally holds the ability to change the rules of the game. Without this owner the cats are completely useless.
What is the benefit game-wise to trade the cats on a public blockchain? To an outside observer it seems like the users have to pay transfer fees at the order of a dollar for no particular reason. As long as someone controls issuance (which is completely reasonable for this type of game) they could just track ownership as well which would be trivial to scale.
I guess it's convenient not to have to deal with a payment processor when selling the kittens. I'm not sure how happy PayPal et al would be to take their business.
From 10 years dealing with different type businesses doing Paypal... they will approve you by default and unless you selling something from their prohibited items list, they will only care about dispute/chargeback levels. If you behave yourself they wouldn't care and I'm having hard times imagining people trading virtual gifts, such as in-game skins, to trigger lots of disputes, because that would eventually ban their PP account rendering them unable to purchase more in the future.
What is the benefit game-wise to trade the cats on a public blockchain? To an outside observer it seems like the users have to pay transfer fees at the order of a dollar for no particular reason. As long as someone controls issuance (which is completely reasonable for this type of game) they could just track ownership as well which would be trivial to scale.