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C&C is representation of GM interacting with player.
Everyone fucking points D&D books and systems but they fucking forget GM. GM and players are what makes RPG not which systems they are using. Interaction between GM and players is what makes something RPG or not. Better or worse RPG isn't due to system used but experience of GM or wait for it... wealth of choices presented by computer game to player (emulating good GM).
Computer RPGs TRY to recreate that interaction between player and GM by building scripted interactions.
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RPG. Role Playing Game. It requires GM and players or representation of GM in form of script or something and players.
On other hand you have Heavy Rain game which is totally RPG as game presents you shitload of meaningful C&C (i don't talk about button presses), The Void/Tension that gives you complete freedom not only in how to tackle events but also which ending even could be said is "good" and few other not named RPG because progression mechanics were not something developers had in mind. While Heavy Rain is shit generally The Void is one of the best games ever.
I've played
The Void/
Tension/
Turgor, and without commenting on the quality of the game (which is a separate issue from which genre it belongs to), the fact that you call it an RPG is an excellent example of my point about people seizing on one particular aspect of RPGs and insisting on using that one aspect to provide a definition of the genre in contradiction to all game mechanics. Though here you're slipping between using story-based C&C as the single criterion defining RPGs (
Heavy Rain) and using non-linearity as the single criterion defining RPGs (
The Void); I don't recall
The Void having much story-based C&C beyond choosing which girl to help, though it's certainly an extremely non-linear game in terms of structure. If you're now using non-linearity in overall structure as the sole definition of an RPG, then the only reason not to include games such as
Civilization or
Master of Orion as an RPG would be that you aren't playing a character (which itself is an additional criterion), and you would certainly need to include games like
Sid Meier's Pirates! or
Megaman --- while dungeon-crawlers would largely be excluded from being RPGs.
As for story-based C&C, here we see the replacement of actual RPG mechanics, especially those that can be performed relatively well by computer games (tactical combat, logistics in exploration), in favor of something that is not only extraneous to RPGs but that is also performed quite poorly by computer games, given the lack of flexibility and extemporaneity in any game controlled by the strictures of a computer program relative to a tabletop game governed by human decision-making. Attempts to use scripted interactions to provide story-based C&C result in the denigration of actual game mechanics in favor of CYOA-style picking choices from a list. Using this as the sole criterion of RPGs would not only add many games from disparate genres but also a multitude of things that aren't even games to begin with (Choose Your Own Adventure, Interactive Fiction), while excluding most games with RPG mechanics on the grounds they either lack story (
Rogue,
Wizardry,
Dungeon Master, etc.), have no story-based C&C (most JRPGs and many other RPGs with a substantial amount of story), or have too small an amount of story-based C&C (the
Souls series, including
Bloodborne).