Has anyone ever run a roleplaying game that was NOT an Action/Adventure story?
No.
Cthulhu is the closest thing I can think of to non-Action/Adventure, but even that tends to include some adventure story elements.
Some? Sorry, but it seems to me to be all action/adventure elements. I suppose there are some instances of horror genera stories that are not action/adventure, but I can think of no instances of CoC that would fit that description. I feel I'm not speaking your language here. What defines action/adventure for you? What wouldn't be one?
A game that wasn't action/adventure would need to:
a) Not feature violence as a mode of conflict or conflict resolution. The characters might work in an ER, and occasionally treat the victims of violence, but wouldn't settle disputes in this manner.
b) Not feature the PC's directly under the threat of violence beyond the sort of accidents or low level arguments people ordinarily face.
c) Would focus on things that are ordinary and mundane. Normal domestic life, for example.
d) Would focus more on how characters feel than what they do, or at least as much on how they feel as what they do.
e) Would be primarily trying to engender in the players some feeling other than excitement or anything related to it (fear, for example when we are speaking of something other than anxiety or nervousness).
I think there are systems that might occasionally tread outside of the action/adventure genera for extended periods depending on the group playing them. Blue Rose, for example, could play that way for an extended period, as could My Life with Master. In theory, many of the World of Darkness ':' games were aiming for that, but I think in practice seldom achieved it. A lot of indie game seem intended to play largely outside the action/adventure drama until reaching some sort of dramatic conclusion, where they switch focus.