Honestly, my main motivation here is to pick all of your brains to see how many different category-words there are, then change my game plan to react to the natural language words. For example, if we didn’t have words more specific than Animal, Plant, Fungus, and Bacteria, I could slap a four-color mana system on that and call it a day. Obviously that’s not the case, but in the unlikely system that I can describe all of creation using only 20ish names i could imitate Cardfight Vanguard and make them into a sort of clan system and do lots of clan-exclusive comboing off each other. Any more than that, I imitate Magic instead: certain cards care a whole lot about types (e.g.: Kavu you control are red in addition to their other colors, Red creatures you control have haste) while others pay more attention to subtypes (e.g.: Tap 12 Allies you control: draw a card) and other just don’t discriminate, affecting everything or nothing.
My justification for calling octopi fish is that I asked a pre-schooler what kind of animal an octopus was, and he told me it was a fish because it breathes water and swims in the ocean. That said, maybe cephalopods could be their own type because they tend to be solitary, which would be thematically relevant to why they wouldn’t combo off each other.