As I said in a prior post, many treat movies, T.V. and plays as literary, because they portray written words. So does roleplaying. The PCs are written words. Their backgrounds(if any) are written words. The rules governing actions are written words.
Not quite. "Many treat movies, T.V. and plays" not so much as "literary," but, rather, as 'text,' which is a distinction that actual literary theorists do care about. And understanding these media as texts is more of a metaphorical/analogical understanding than a literal one. We should not confuse/equivocate the metaphorical sense for the literal here. We speak metaphorically, for example, of film literacy. No one believes that film literacy represents any person's actual reading literacy of films, but, instead, it represents a person's ability to know, understand, and interpret the intricacies of films and their craft.
The main reason why these media are discussed as "text" is because literary criticism is far more advanced chronologically than other burgeoning forms. Literary criticism dictated the terms of conversation, and many of the earliest film studies academics came out literary studies or imported their terms from literary studies. Film studies was largely discussed through literary criticism until the discipline began establishing for itself its own identity, idioms, and issues as a field. We probably should not claim that films are literature simply as a result of this historical accident.
So if you think that "many treat movies...as literary" it helps to appropriately understand how and why that is the case. Furthermore,
treating something as literary does not necessarily mean that they are
regarded as literary.
In TTRPGs, characters are far more than their representation on a character sheet. (Some players might even be offended by such an insinuation of their characters, since their characters are also their histories, actions, and words that may never one be committed to the written page.) Whatever rules may govern their actions are trumped by "rulings and not rules" (per 5e) where the DM frequently acts as a metatextual authority that exists above and beyond any notions of a governing text which implies that RPGs relegate the literature to a marginalized or less privileged role in the RPG process. (Here I would again note the parallel between cooking recipes and RPG rules.)
Max, one of the problems with your argument is that while you are doing a wonderful job arguing that texts exist as part of RPGs, which has never been in doubt, you are not doing a good job arguing that because RPGs utilize literature and text that RPGs are therefore literature.