The way I see it-
A game is a system people use to entertain themselves and increase their happiness. That's what a game is- for. And the further away from that a game gets, the more I ask myself, "Is this really a game?"
There are in general, two types of players.
Casual and Intense
The Intense player really cares about what's going on. They're deeply invested in what's happening in the game, and are generally the ones who 'win'. These are the people who like to accomplish things and get a great deal of happiness when they do so.
A Casual player cares more about the entertainment value of the game. These are the type of people who would be fine just sitting back and watching a movie. They're less about winning the game and more about just kinda, watching things happen.
The amount of fun a person has playing a game depends greatly on that person. An Intense player needs clear goals, and something of a challenge. A casual player needs some sort of entertainment. Whether that entertainment is the story, or the other players. Naturally a player looking for entertainment will have less fun in a challenging environment. Even more so if they're tired. The amount of effort a player desires to put in to achieve a result changes depending on that player.
A story gives a player goals and direction, and if it's good enough, it entertains the player at the same time. Some games don't really need a story. If you're game involves throwing a ball into a basket using some sort of QWOP functionality, naming the main character Joe and giving him a tragic backstory doesn't really do as much. Most of the entertainment value in that case would be in watching the character flip over backwards and spasm on the floor.
