Ever since polygons were easily generated on computers, players have played games that only allow control over a 2D plane, despite the graphics suggesting something more.
Despite the ability to sidestep, Tekken is a distinctly 2D game in terms of our avaters' interaction with the world. Clockwork Knight* was a 2D game as well but here the polygons were used for a more interesting purpose - giving clearer signals to the player.
Despite the inability to interact with the 3rd dimension, seeing a giant object falling out of the background towards you served a vital purpose - clearly telling us that for a certain moment, standing in a certain location would be harmful. Thanks to the clear real-world parallels (who would stand underneath a solid falling object thrice their own size?) and our familiarity with the falling of an object, the moment of danger and the dangerous location are both quickly understood - something that may not have been the case if, say, a spiky block was to fade in then flash out.
Just as some games use 3D graphics to give a representation of what is about to happen on the 2D plane, so too could some games usea 2D plane to represent what is about to happen on a line.
In the flash game Train Robber, we only have influence over one line (moving our character left/right) but seeing the moneybags' motion in the 2D plane allows us to better predict what part of the line they will fall at. Imagine if the game had objects fading in on the line, reaching full opacity at the moment they were 'collectable'. Not only would this remove the challenge of quickly understanding lines of motion but it would replace it with a near-unreadable visual system - discerning slightly variations in shade being far harder than variations in position to our human eyes.
Similarly, in my own (still unfinished) Pico Jr Jr used bouncing and flying enemies to show the exact position where the avatar could either be killed or meaningfully fire into at some point in the future.
Each player in Pong can only move along a single line, but the 2D graphics are vital to not only show where the ball will arrive but also show the relationship between the portion of the bat hit and the angle the ball reflects at.
Space Invaders is a 2D game in my mind despite the limited motion - the projectiles we fire interact with any part of the plane and so the position of enemies becomes meaningful - not just as a way to inform us of what portion of the line their projectiles will reach but also to inform us when to fire our own projectiles - we need to quickly evaluate several factors including projectile speed, enemy motion and current enemy position.
It's probably no accident that the first popular videogame is played along two lines - Computer Space proving too much for most.
The removal of time as a factor has certainly opened up gaming as has the reversion to 2D gameplay. But what caters to those who want to still test their ability to judge timing and think quickly, without the complexities of 2 dimensions?
One-dimensional games could allow us to provide new complexities for existing gamers when the spatial ones are removed or simply make more accessible game that remain fun - adding the varied levels and lush graphics we expect of modern games.
It seems an unexplored vein and for them to remain so would surely be a shame.
*I'm sure there are many other examples of 3D element being used to signal events on the 2D plane - including Yoshi's Island. I apologise for the lack of research and thoroughness in this article.
**Programming by Danny. The game definitely has some issues - mostly the fact that the 'rhythm-based' element devolved into clicking frantically. But that's neither here nor there.