Because GPT-2 in its current form isn't that great at keeping track of facts (like the player's inventory or skill points) over the course of long conversations, or at consistently enforcing rules (as the OP's blog post demonstrates). Allowing a more logically stringent system to handle those parts of the game might produce more realistic results.

Because of the lack of manual structural elements, there basically aren't any explicit rules for how the world works. In practice this means that the stories sound more like a fever dream, the AI will let you do almost anything, and story beats are sort of coherent moment to moment but the arc of everything makes no sense.

It doesn’t have to have structural elements, but it does need a constraints system.

You: I kill all of them and become an immortal god.

Game: No, that doesn’t make sense. You can’t just kill everyone; you can run over and attack them, and see how that goes for you if you like...

Without constraints it’s not a game, it’s just telling yourself a story.

...nothing wrong with that, it’s fun. ...but it’s not a game imo, any more than giving someone a blank piece of paper and a pen is a game.

Agreed, it would be more interesting if it could dynamically construct the rules and paradigms of the game. It would be like playing a new game every time.