It's like fighting off an Evangelion or Angel using a slingshot. The graphics is pretty phenomenal when you consider a limitation of 4 colors. If the game is also supposed to be minimalistic, it also meets that goal.
In terms of controls, I agree that a pause option, replay option, and a mute option would be welcome. They are kind of par for the course for even this sort of minimalistic game. Additionally, the use of the slingshot and the perspective/physics of it, while they made sense once I knew what to do, weren't exactly intuitive. You don't have to hold the player's hand, but at least give them rudimentary directions. For a while I thought I was supposed to be clicking on those tumbleweeds, or the cube, or something.
In terms of objectives, having levels wouldn't have hurt. You already have the engine in place, why not have several enemies that come in waves? The city could be 'rebuilt' each time or something. Having just a cube to defeat didn't seem ambitious. Especially with the odd difficulty curve. If you can't figure out the slingshot, the cube is hard, but it's actually not too difficult.
In terms of other execution points...the cube seems to be invincible while horizontally transitioning from a destroyed building to the next, and also while it is mid-pound. This seems like a bit of lazy programming or something, since logistically it shouldn't be invincible at those times. I'm also curious if the slingshot action couldn't be animated a bit better, since it's definitely got the most lazy graphics and animation with the string.
Good game, cool and unique (comparatively) gameplay idea, and slightly botched execution that still delivers a playable and quasi-challenging game.