Lots of people - perhaps the majority of would-be game designers - think that gameplay is (or should be) reduced down to "telling a story" in the player's mind. This is seen as some kind of way to reconcile the "ludic" and "narrative" camps. Unfortunately, it's wrong.
Before you get me wrong: games can and usually do have stories. These stories add a lot to the game. They can even control the gameplay. But they are not, in and of themselves, gameplay. Gameplay is the stuff that happens between cutscenes, remember?
Now, gameplay and story. Story is an idealized example in an idealized world. Gameplay is a concrete example in a concrete world.
In a story, the full rules are never spelled out or even internally represented. The story itself is not governed by strict metaphysics of progression or content. This is because we want to be able to say things like, "she killed the dragon" without mentioning the eighty thousand tons of dragon shit over in the corner. We want to skip the bad stuff in favor of the good stuff. Hence, idealized.
In gameplay, the experience is governed by concrete rules which, even if not explicitly explained, are implicitly ingrained. IE, you cannot simply make a grenade go winging off into the sky and blow up the sun - unless the game's rules specifically allow for it.
You can still get some impressive stuff from gameplay. But you also get stuck with the eighty thousands tons of dragon shit. For every moment where you kill two zombies by throwing another zombie's head at them, there are a hundred moments where you are simply shotgunning yet another zombie.
Some designers seek to minimize this. They want every moment to be new and unique. They want to write a story that the player plays through.
That's not a game.
These designers totally misunderstand the nature of "gameplay". Gameplay is when you're given a set of rules and allowed to navigate them. There are inherent rewards and punishments as you navigate, and the power of gameplay lies in the way a player seeks to do his best.
Sure, TimeSplitters 2 had roughly a zillion zombies in it. Hell, it had three challenges which were nothing more than shooting and/or punching as many zombies as possible. As a story, it would be quite dull. You'd edit it all out and turn it into an action-packed thirty-second fight scene which plays nothing like the game ever did.
But the game is fun. It's entertaining. It's stressful. That's because the player is navigating the rules to the best of his or her ability - not simply making up or listening to an idealized version.
The strength of gameplay lies in that territory. It's not about making a story. If it is about making a story, you've made a tool, not a game. Nothing wrong with that. The Sims was part game, part tool.
But in order to get the game, you've got to let the player make concrete examples in a concrete world. You've got to give them the rules and let them dance with those rules. That's what a game is: dancing rules. Those rules stand on their own, and are not about stories.
In fact, the deeper you go, the more it appears stories are about them.