I'm not sure how you can think that, as my statement was about "specific code for each scenario". Your statement and example is about rules for a single action. You are arguing about a single action; I am arguing about a set of actions.
Fist, this seems like one of those cases where bad definitions are leading to confusion. I'll attempt as best as I can to concede your definitions for the purposes of communication, but ultimately I don't think they are coherent. I don't think "a set of actions" in this context has a lot of meaning. In Nethack actions are taken discretely. There isn't really any meaningful concept of "a set of actions" except in the mind of the player. Players can exercise creativity by performing a series of actions but they can neither improvise (in the sense of doing something wholly new) nor can the program itself improvise. Further, by this point in the code's refinement, pretty much any sequence of actions has been discovered and pretty much any circumstance that a sequence of actions could create has been studied and thought about and if warranted special handling for the circumstance is added. For example, entering or leaving a shop by means other than the door is handled. For example, if you dig a hole in the floor you can leave the shop and won't be charged with theft unless you carried out an object or an object fell through the floor with you. That your pet can carry out an object out of the shop without flagging you for theft isn't improvisation, but designed behavior.
Let me iterate: I believe that coming up with a scenario by combining known rules in a way that was not previously planned for is improvisation.
But even by your own definition, the computer can't do that. For one thing, the computer has zero understanding of the sense of anything it does, and that puts it in a very different class of language users and tool users than a human. The computer can't handle any proposition in any combination except what it was programmed to handle because it doesn't understand the sense of any proposition. A human can propose to both jump and kick in the same action. In nethack you can't even input that proposition much less expect the computer to handle it. A human could resolve the improvised "jump kick" action because it understands the sense of both actions and attempt to handle.
And neither can you or I come up with new regions to explore that we have no knowledge or understanding of how to provide. I think maybe this is your key logical error -- for a computer to improvise you require it to create things it knows nothing about, but for people you are content that they combine things from knowledge they already have.
You seem to be attempting to argue that there is no difference in the improvisational skills of a human and the nethack program. But the key logical error you are making here is the nethack program knows nothing. It has no sense of anything. So it can't combine anything from knowledge it already has because it has no knowledge. Thus your point about you can't improvise unless you know something while it is true also misses the point. I actually know something. Nethack has zero knowledge.
To see what I mean, let's not focus on what a human and a computer program both can't do but what a human can do that a computer program could not. And the obvious example is suppose that Nethack was a pen and paper game using the rules of Nethack. Then the human GM taking the computer's role could decide to add a Kobold town as a branch on the second floor, and an orc town as a branch on floor 7, and a dragon's lair branch between floors 15 and 19, and 4 different branches of Hell reached via a new river Styx set of maps, and any other things by combining elements from the game in new ways. He could also choose to add new monster variants and rules extensions. He can improvise all these things because he actually understands what an "elf" is and what game they are playing. The nethack computer program has zero understanding of the meaning of what it does.
If you apply the same definition of improvising as you do to netback, then you you should be able to fulfill this request:
Create a new region for the game @Gorgon Zee is currently running, including descriptions of the environment and things that tie into their player character's backgrounds.
I believe this fits your description of what Nethack cannot do (and so cannot improvise, according to you). So for your definition to hold water, you have to show that it's actually possible to do at all!
Do you see why this is spurious? I agree that you can't improvise without understanding, but that doesn't in any way impact my argument. I don't need to show that it is possible to improvise without understanding. I just need to show that there is a difference in the degree of understanding. For example, I was fully willing to agree that a LLM has some understanding in some sense and so can improvise to some degree. Exactly how much understanding a LLM has and whether it understands either the sense or meaning of a word is a matter of debate. I don't think we know and we are just beginning to understand how the apparent understanding of a LLM emerges. But the idea that there is no difference in the improvisational skills of a program like Nethack or Balder's Gate and a human GM is ridiculous, and the idea that handling a series of creative move choices using the rules is improvisation by the GM rather than the player is equally ridiculous.