I quite like this style.Maybe a simple shooter/bullet hell kinda thing, you have the screenspace for it. Basically you could just shoot in the direction you're moving and hold up to shoot upwards. And just horde increasing numbers of enemies into it and the player has to survive as long as possible. As your world seems broken up into screens you could count each screen as a level, and the player progresses by beating all enemies and then moving out, you can add random interesting things to look at on some of the screens (like monument or something, would add a little exploratory factor to it).