Just wondering, what's the lore?
Half of the game in my opinion is the storyline - and I mean something more than "You're a brain, you found a planet, now ♥♥♥♥ colonize it."

In my opinion games shouldn't have stories.

Or storylines could be optional, like in ye oldie nes games. Metroid, for example, starts you on an elevator, and you do things just because.

Depends on what you mean by stories. Even games like chess, which is CCs distant ancestor, tell stories, it's just not the same story every time. In the case of chess it's the story of a battle, each piece has a name, function and art design informed by that name (the name of the queen until the 15th century usually not the queen but rather some kind of leading military person). So the story here is really in things like what names the factions have, how do they look, what kinds of guns do they have, etc.. I mean if there is no story behind who the Dummy Corp are, why even call them the Dummy Corp or make all of their dudes look like crashtest dummies.

Stuff like this provides context to the player and makes them care about stuff in the game rather than just looking at it like it's just numbers being crunched in a computer at high speed in order to achieve rapid interactivity.

What I mean is that everything should rise from the system.

Game of chess isn't a story of a battle. It is a battle.

You can find stories to tell in games; but a game with a story is chess played to already written moves.

That's a bit like saying a novel or movie shouldn't have any antecedent action. Like Superjuden said, it establishes a frame for the story and helps some players enjoy the game more. It's almost always optional, so why rule it out?

This is an example to show what I mean by story:

Ocarina of Time has a story, Mount&Blade Warband doesn't.

So you mean the game shouldn't have a pre-written plot? Why? I mean, for Cortex Command, that makes enough sense, since the focus is on emergent gameplay. That doesn't mean every game has to be that.

And OoT would be better off without a story? All I see in OoT without the story is a completely desolate world where a player just wanders from area to area solving various puzzles and fighting some enemies without any reason ever given other than some pointless goal of beating the game.

Do you also think this story-is-not-for-games is also true for the RPG genre? Do you think any of the Fallout games would be better if all story was removed from the games.

I can get what Crow is saying, and he is partially right, he's just not entirely understanding the importance of plot.
With the exception of sandbox games, most games are created with the sole intention to tell a story, while game mechanics are incredibly important to a game, most games would fall apart without a story.

To keep with the OoT example, The 'game' would still be playable with only a bare bones gameplay of 'hack your way through enemies till you get through the temple', and if they took out gameplay completely you would be left with a bearable novel. But if you took out the story, you would be left with a Portal style series of test, except without the humorous narration, or any desire to escape, or even the promise of cake. Essentially, if you took away the plot you might as well be playing an over glorified version of chess, something which I believe video games should not aspire towards.