It depends how you divide between what's universe and what is story. The Fallout universe has me hooked but the playable stories are unappealing to me. The custom universe/rules me and friends play to a Risk board is the reason to play, I can't imagine trying to force a story into it. I'm finding it hard to think of board games with actual predefined stories to follow, they usually just have a universe to play within.
Interesting stuff. I believe in every game there's a mix of a competition, exploration, collection, skill and emotion present. In board games and massive online universes, a social element is also important, enabling alliances and cooperation. When a game contains a distinctive style or atmosphere, it's easy for a player to immerse. A proper storyline is essential for games that are not solely based on skill. It will enable the player to identify with the hero and care for hi