"in any form of interactive entertainment you've got the system (rules) and resulting discourses (which can be remembered as stories)."
What we have here is a failure to communicate.
Play a game.
As you learn how to shoot zombies, are you "telling yourself a story" or "remembering a story"? As you zoom through a race course, are you "discoursing"? No. You're using a much deeper part of your brain - one which doesn't use language or, in fact, linguistic idealization. It is simply, and deeply, about pattern analysis.
Can you make a game which is about telling stories? Sure - Baron Munchausen is such a game. Can you make a game which has unreliable rules? Sure - Lemma is such a game.
But there is a fundamental difference between experiencing a story - even an interactive one - and experiencing a game. The story starts and stays idealized and rule-less. More accurately, the rules are a mish-mash of whatever rules the author(s) have in their brains, and fade in and out as mood demands. It is not about manipulating a pattern using rules so much as manipulating a tide of vague pattern-like preferences using a lack of rules. That doesn't make it inferior, but it does make it different from a game.
A game has a concrete set of rules and the player's jollies come from manipulating them. It's a wholly different method of pattern analysis. It's non-linguistic, non-memetic, non-aesthetic. Even if it is represented by language, aesthetics, or memes, the actual pattern recognition - what to do when - is not.
For example, "I can make Suzie fall in love with Jack" is a story, but the actual knowledge of how that can be accomplished - and the fact that it can be accomplished - is not a story. The story, in this particular case, results from having learned the rules of the engine... a process and knowledge which is not a story, although the actual act of learning may be considered one.
Without patterns of rules governing your progression you allow the player to do anything. There's nothing wrong with that, but it is now officially a tool, enabling the user to make whatever he wishes within the capabilities of the tool.
A TimeSplitter's gameplay session isn't "remembered" as a "story". It's "remembered" at a deep level, in terms of how to move, how to shoot, what weapons work against which enemies, the layout of the level. These are often not even "conscious" memories, certainly not "stories".
Sure, you may remember gameplay fragments which you could stretch the definition of "story" to cover, like "damn it, those invisible guys are so irritatingly difficult!" or "I just killed two zombies with the head of another zombie!" But these are exceptions.
What many people - evidently including Patrick - are arguing is that these exceptions are inherently better and more entertaining than the rest of the game, so the whole game ought to be made of them. This is, unfortunately, both wrong and impossible.
It's impossible because "cool" is always cool relative to something. If every throw of a zombie head kills two zombies, it's only cool when it kills four zombies.
It's also wrong, for much the same reason: in order for a player to manipulate the pattern, there needs to be a great deal of that pattern in all sorts of states, so he can learn. The player learns to shoot. Then, instead of simply wanting to hit, he wants to get all head-shots. Then, instead of wanting simply head-shots, he wants to get entirely wall-bounce head-shots. The progression towards this goal is the fun of the game. Simply skipping to the wall-bounce head-shots defeats the purpose.
It doesn't defeat the purpose in a story sense. It could be an awesome story moment. But it defeats the purpose in a gameplay sense. If every shot miraculously kills everything in this absurd way, there's no gameplay in that. Unless you count watching them explode in various ways as "gameplay".
A story world is a questionable situation, because nobody's really made one. How much is it a story creation tool? How much is it a game? Does it have concrete rules, or does it let you go and do whatever you want?
Obviously, there's a messy situation in the middle, where it's a game until the player decides he wants to override it or ignore the rules. However, at a core level, the distinction remains: it is a game so long as the rules are followed and the pattern manipulated according to them.
That is the difference! I hope I'm being clear, here: a story is an idealized example. The joy of a game is in the concrete. It's on a wholly different level.