Language-Games and "Language-Game"

By Wittgenstein's own definition of it, the meaning of the term 'Language-Game' varies according to the Language-Game in which it appears.  For example, in the Language-Game 'Refuting Russell', it is defined as a relation between words and actions.  However, in the Language-Game' The Origin of Language', it can be defined as a relation between people and words.  To put it less obliquely--it is a familiar fact of experience that the meaning of words can be a function of the degree of intimacy of those conversing, with the possibility that every new interaction constitutes a unique Language-Game.  On that basis, Wittgenstein's concept of Language depersonalizes Communication as much as does Russell's, regardless of how effectively it debunks the privileged status of Logic entailed by the latter.