What do I mean by "conditions needed to be a language". Gödel aside, many game systems may appear language-like, but are ultimately just symbol processing: a language requires self-referentiality. Human communication has existed for some 2 million years, but it was only the evolution of recursive elements some 70,000 years ago that enabled what we recognise today as languages (see The Romulus and Remes hypothesis). A designer's ability to alter the game design is similarly self-referential, the addition and change of game rules are the kind of metaphoric extensions that we see occurring in natural languages.
My realisation today is that by considering a game design to be a natural languaage, the design in turn influences the designer's perception (the weak Sapir-Worf hypothesis) in ways that are not under the control of the designer.
Why are games so good at assigning meaning to symbols -- a 4 kilobyte roguelike can give layers of meaning to a single ASCII symbol ----, while much more complex and process intensive systems like LLMs fail so miserably at this? I now suspect that it's this linguistic
design layer that the game grows itself from that gives games much of this power.