Several ways here it works:

1. You develop a fun play mechanic (or set of play mechanics) that you put into good level design that ramps up well, and is executed well (think Tetris as an example).

2. You create a sandbox environment that is procedurally generated that the player jumps into and creates their own path.  Sandboxes can be in the case of massive-multiplayer online RPGs with no set story to follow, sim/god games where you transform the world, or a dungeon crawl like Nethack where the goals are to level up your character.  Borderlands woulod also fit into the last one.

3. Provide multiplayer games which have goals for the players to accomplish, even if it is something as simple as getting to a finish line first or fragging more opponents than you get fragged.

There may be others.  In the former, you are in the area of arcade games, and you can give the players goals they try to accomplish, with fun play mechanics.  In the later, you give the players a rich enough environment where they can chart their own path and make their own stories.  The game doesn't come with a story, but players provide it.  In the last one, it is based on human competition.

It's true that Pokemon's story kinda sucked, but it still had one.

Of course you can have a game without a story. There are tons of games that focus solely on gameplay. However, I applaud the trend of adding both RPG and story elements to the other genres. Especially adventure games. Heck if they aren't going to have at least a minor story in an FPS they might as well cut the solo mode out altogether.

That looks more like an platformer with some digging.  Miner: Dig Deep is more like Dig Dug, without the monsters and some RPGish grinding thrown in.  The board is different each time you play.  It doesn't have levels, per-se (it doesn't even have level design).  You can beat the game and go again, with your equipment you had for the prior run.  I am thinking the best way to describe it is an arcade resource management game.  Here are video on it:

Starting out:

As you play through:

Speaking of biscuits, do biscuits need stories?

How many of those in the top 10 actually have stories?  What is the storyline behind Wii Sports?  And does Super Mario Bros. have a story, or does it have a goal (rescue the princess)?  If a goal is a story, does that make a grocery list a novel?

Are we better off if the stories suck?  I will agree if a GOOD story, properly told, is there, then things will likely be better.  But if the story is poor, then you have to rely on gameplay, and other reasons to play, to compel you to play.

Games are given quite a lot of latitude. Take graphics for example. There are plenty of good games out there that don't have the best graphics, even for their time. However, to reach the top of the pile a game pretty much needs both good graphics and good gameplay.

If we look at the top games in each genre we start to see some patterns. For RPGs its obvious, good gameplay, good story. For adventure and FPS games its good graphics, good gameplay. Platformers still uniquely seem to stick with gameplay.

The point is that different genres have one or two things that they _must_ have, and in some of those genres its the story. In some cases whether a story is poor or good doesn't make a lick of difference.

Some games need story. It depends on what type of game you want to make. If you want to tell a story through your game, you definitely need one.

Not all games are simply about "haha let's have light-hearted fun". You seem to generalize in a way that suggests that no game would need a story. As if no game were ever designed in order to tell a story. Which is an erroneous assumption. It's as if you're trying to limit the definition of games to "gameplay-centric games only", passing off everything else as something completely different, not even a game.

A good example is Shadow of the Colossus. I don't like it mainly because of its gameplay, but rather because of the entire experience. The amazing surroundings just there for you to explore, the atmosphere created by the music, art, design, and subtle story, as well as gameplay. Remove any one of these elements and the game falls, because the experience that the creators are trying to achieve wouldn't be complete. The game doesn't even have much of a story, and you can definitely neglect it, but you wouldn't get the same full-fledged experience. You get my point?

11 pages of this.

Game = competive activity with a set of rules to determine a winner and loser. VG can be games because Mario competers against Goombas, turtles, bowsers with a set rules to determine a winner.

All VG are games. since they all have a set of rules where players compete either against other players or AI.

There is no story in that definition.

Thus games do not need story. If people aren't touching games because of lack of story. Then it's not the game they are interested in as it is the story.

11 pages? good lord.