The words play and games have a unique relationship in the English language. There are two ways to frame their relationship, both of which are useful:
Games are a subset of play: The category of play represents many kinds of playful activities. Some of these activities are games, but many of them are not. In this sense, games are contained within play.
Play is a subset of games: Games are complex phenomena and there are many ways to frame them and understand them. RULES, PLAY, and CULTURE are three aspects of the phenomena of games. In this sense, play is contained within games.
A game is a system in which players engage in an artificial conflict, defined by rules, that results in a quantifiable outcome. The key elements of this definition are the fact that a game is a system, players interact with the system, a game is an instance of conflict, the conflict in games is artificial, rules limit player behavior and define the game, and every game has a quantifiable outcome or goal.
A puzzle is a special kind of game in which there is a single correct answer or set of correct answers. All puzzles are games.
Multiplayer Role-playing games (RPGs) do not clearly possess a quantifiable outcome. Whether or not they fit the definition of a game depends on how they are framed. As with other open-ended game-like experiences such as Sim City, RPGs have emergent quantifiable goals but usually no single overriding outcome.