To me this seems like one of those arguments over which of Association, Gridiron or Rugby football ought to be considered the 'real' football (based on one or another physical or historic quality of one or another of the sports). Or maybe someone loudly advocating that the necromancers in a game aren't 'really' necromancers because all they do is animate corpses, not communicate with the spirits of the dead to divine secrets and foretell the future (like 'real,' non-fantasy-genre necromancers might). It seems incredibly pointless to my mind because, quite frankly, sometimes a word is just a social convention.
There is a recreational activity we all partake in. It is, socially if by no other metric, a distinct category from board games and their ilk, Improve acting, larping, computer RPGS, or any other past time; and at the same time a cohesive whole (if only in that people regularly switch between them during time set aside for playing one of the whole). I'm sure there are several incredibly long-winded arguments pertaining to how '(Table-Top) Role-Playing Game' is not the most perfect term to describe this category of activities, each hinging upon some highly technical facet the argument-crafter and at least three other people consider of-most-primary-concern. However, that is the term that has been taken by the community of this activity (and society in general). Trying now to argue that one or more of the group of activities shouldn't technically be included by the term doesn't actually improve what is communicated by using the term.
