Framework for a taxonomy of gaming

Working definition of a game

A game is any contest or effort (play) among adversaries or teammates (players) operating under constraints (rules and resources) for an objective (winning, victory, prestige, status, or pay-off). The exercise, or activity, should involve overt competition, or cooperation between the individuals or teams, who are competing against each other, or together fighting the odds, while conquering circumstances (nature).

Functional classification of games:

The generic architecture of fully-fledged games is illustrated below.

For more details, see Chapters 2 and 5 of the book: 
Magic Circle: Principles of Gaming & Simulation