In a sense. However it is not necessarily restricted to dungeon delving; OSR games should handle just about any situation you'd find in any other game or setting. And yes, you don't set out to tell a story that the GM has planned out, but it can certainly produce wonderfully interesting stories that come about as the result of play - the interactions of the players and the game world as portrayed by the GM, even if that takes the form of a bunch of anecdotes stitched together. Often stories you hear from OSR sessions sound so strange and creative that there's no way it could be the result of a planned narrative.
Another difference is that "solving" a problem in an OSR game does not have a number of discrete solutions that are codified into it (though roguelikes tend to allow a greater range of potential solutions than other types of games). Instead, the GM should be open to those wildly creative methods of solving problems formulated by the players. Often, a GM doesn't even know how a particular problem could be solved when they create it.