@evo: "Transcendent" is probably pushing it, in retrospect. I enjoyed BG&E a lot and occasionally find it hard to articulate precisely why, and I think it's as much for the minor stuff as it is the major. A lot of my favorite games give you some clear story goals to chase and then a lot of little optional tasks, many of which are mini-games governed by their own rules. Dark Cloud 2's another fine example, and I'm usually content to call that one my favorite console game of all time due largely to its versatility.
As for what constitutes a mechanic, you're right in that it's a gray area. Infrastructure like pausing, menus and stuff like text input all falls under a different stage of the development process, but they're all conceived by game designers and implemented by coders like everything else. (Once you're in game development, there'll be a fun task where you'll have to visualize the entire menu system of a game all expanded out like a flowchart, making sure there's always a function to go back one level and so on.)
For me, the mechanics of a game encompasses everything that allows it to function as intended by its designers, including perfunctory things like saving the game or turning on subtitles. Also, you could always argue that inputting your initials is an important end stage of the classic Arcade gameplay experience, or how writing a character's name along with the rest of the character customization process is an integral part of any role-playing game with player-made characters, but those are definitely debatable.