I really hate the word "depth" or "soul" on videogames, kind of a buzzword since it too dam subjective.
But in my opinion what you are describing is more the presentation itself of the game, the visual style. In games, gameplay ande level design is what gives the depth to games in my opinion. A game like mario is rather simple, run to the left and jump, but there a whole tought behind this concept, which way to take (up down) wich item to keep, wich world to choose, where secrets might be,where to attack and when to dodge. A whole mix of toughts and sensations that change constantly behind the simple idea of run to the left.This is, in my opinion, the depth of mario. But i understand people might figure depth as a more artsy thing.
About the chessynes, cant say it hasnt been there since the beggining. The idea itself of a plumber rescuing a princess form a turtle dragon is already cheesy.
