Let me modify your analogy a bit: the phenomenon, or the appearance, is like a video game. It includes what you see see and hear, and how the game responds to the controls. The noumenon or the thing in itself corresponds to the program running the game. Playing the game will not let you know details about the software (what are the variable names, are the monsters in a list or a hash table, etc.).
For that matter, you can't even know that different phenomena within the game have consistent noumena. One monster may be a complex data structure with its own AI controller, while another is just a sprite that pops up and has no influence on the game.
Kant's philosophy can be understood as a claim that the world is like a video game. We only have access to the video game; efforts to figure out the program underneath are inherently and eternally hopeless. In the video game analogy, you could imagine ways to get information about the underlying program by going outside the game, but in life, you can't even do that because any sensation you have is necessarily just the video game.
Now imagine a video game with no causal connection to the controls. It doesn't matter what buttons you press or what you do with the joystick, it has no effect on the game. It wouldn't be much of game, would it? The notion of the controls affecting the game is a precondition of having a video game. The same is true about time. If nothing changes in the game, or if it randomly flashes from scene to scene with no connection between scenes, it's not much of a game. The same is true of space. If the video game were just a single point of light, it wouldn't be much of game. Causality, time, and space are essential preconditions to having a game at all.
Kant's theory says the same thing about life. The very possibility of us learning about the world depends on causality, space, and time. Particular events can be different and still make it a game. You could replace elves with Martians and it's still a game. You can replace realistic physics with something more exotic and it's still a game. You can even replace the kind of graphics: realistic 3D, anime, toons; it doesn't matter. It can still be a game. But those three particular features: causality, space, and time, are essential to having a game at all.
But notice that those three things are not the software; they are implemented by the software (and the hardware). Kant's theory is that those same three features are essential components of human cognition, but that they aren't necessarily fundamental to reality; they are just the way that reality is presented to us.