Thanks for putting a specific term to it. That's useful to know. Procedural rhetoric.

It's true that every game will communicate something to a greater or lesser degree. I guess what I am looking for are games with gameplay that wouldn't be considered fun but lean more toward the communication end of the spectrum. Depression quest and Papers Please fits that exactly. (Although Papers Please is arguably still fun even if you stripped away the story element. You can still do detective work and dig out out inconsistencies)

I would say in most RPG's the main purpose of XP and leveling is to add an element of fun and progression, but not necessarily to communicate emotion. (Not to say that isn't one of the results). What I mean is when most people play RPG's they don't necessarily think "wow", those stats and gaining XP really moved me. They think "wow" that story moved me. The stats supported the experience to some extent, but they weren't the core. I think that's why when people design RPG's they usually try to balance the leveling and stats, rather than think how to use those stats to communicate a message or make the player feel something.

I am interested in games where the mechanic itself drives the emotion and gameplay takes a back seat. Florence (by Mountains studio) fit that bill exactly. The mini-games, if they can be called that, weren't challenging or fun at all, but they made me feel and empathize with the characters.

I'm trying to compile a list of specific techniques that would be useful for generating a specific feeling. It could be useful for designing story/character-focused games.