I don't think it's very confusing to think of someone who writes out a set of rules to guide the play of a tabletop roleplaying game as a game designer. Their decisions shape everything that happens at the table - what aspects of the experience get focus, what aspects get glossed over, what deserves reward and what that reward looks like ... their role in a tabletop game is very clearly that of a designer.
The idea of a GM as a game designer comes up periodically in GM advice columns. I think we first saw this in the form of blog posts highlighting elements of the Mechanics-Dynamics-Aesthetics (MDA) framework as relevant to GMing, particularly the idea of aesthetics of play; a player who thrives on experiencing discovery at the table is going to want different things out of a session than a player who thrives on performing a role as a character, and GMs are well-served by being aware of what their players want (and what they themselves want) and designing what they create and provide to the players with that knowledge in mind.
A lot less obvious, I think, is that the players design the game as well. Pacing is an element of game design - and the same combat created by the same GM in the same system, for example, can be a tense three hours spent calculating every move to deal with one's opponents as effectively as possible or a single whirlwind hour of snap decisions and adapting plans on the fly, depending on how the players conceive of their roles and how they act within them. Narrative focus is an element of game design - and the same scenario can be a romp from battle to battle or a series of negotiations to muster enough support from all the parties involved to forge a peace, depending on how the players interpret their role within it. Tone is an element of game design - and the same system can produce a lighthearted comedy or a grim struggle, depending on what the players contribute to the story with their choices.
None of the participants in the event of a roleplaying game have full power over it - it is, as everyone always says, a collaborative storytelling - but all of them have some power over it. And I think it benefits all of them to be conscious of that - benefits the authors of systems to know what they want to facilitate, runners of games to know what they want to provide, and players of games to know what they want to do.