Generative AI output that does not fit into the four categories, on the other hand, is common and should definitely be disclosed.
Care to name a few examples. If it is common, there should be plenty of examples. And only because something does not fit exactly in 1 of those 4 categories, does not mean that there is need for a 5th. You can just select both or the most fitting.
Also, if it is the output of a gen ai, but does not end up in the game, why tag it? There is no transitive quality asked here. To put forth an analogy: the cook of vegan food does not need to be a vegan, for the meal to be vegan.
About the puzzle. In case of a sokoban level generated with generative ai, it is code. It is literally a set of instructions. A level is basically code in an unnamed programming language that tells the game, how a level should look.
One might argue, that it is also narrative (dialogue) as well, if you think about puzzles as riddles. Riddles are a form of narrative, but their puzzle nature is more wordy. You could even argue it to be graphics, if you actually used the visual representation of sokoban levels to train an ai and produce more of such things. And if you used an essay generator or a code generator would answer the detail, if you would select text or code. But strictly, a level of any video game can always be considered code.
If the thing carries meaning, it is dialogue/text/story or code or a mix of those. If it is for looks, it is graphics, if it can be heard, it is sound.
(Yes, yes, images and sound carry also meaning. I meant abstract things that only bring meaning into the game. Like the game play, balancing, item stats and so on.)
If it is neither of those things, I am not sure, if you can call it an asset or a thing that is actually in the game.
I wondered about more categories a few times. But if there is one, it probably is not something common or intuitively understandable. And if there is, it probably can be seen as some equivalent of "code".