Chess - Game Design Wiki

Some possible reasons for the long standing popularity of chess:

SimpleAsPossible - the rules (minus a few easily ignored exceptions like castling and en passant) are relatively straightforward. The biggest obstacle to learning is memorizing the movement patterns of all six pieces - well within SevenPlusOrMinusTwo.
DepthOfChoices - I haven't checked recently, but calculating every possible state still exceeds our most powerful computers.
ClearShortTermGoal - capture opponents pieces, avoid capture yourself, and control the board. The line of pawns up front make the first move fairly obvious, but it still holds MeaningfulChoices.
CompellingGoal - while chess has only the faintest veneer of military theme, the goal of capturing the king is simple and very small extension of the basic rules. It is something that could occur at any time, but for the positioning of pieces