Idea One:

God Game. You're a god, leading/protecting a small country. You need your people to build temples and fight in wars, but you also need to sacrifice them to power your Acts Of God. Probably too on the nose

Idea Two:

Platformer. You're a parent leading your family to safety, but every time you would have been killed by a trap or enemy, one of your children takes the hit in your place. Too dark?

Idea Three:

Top-Down 2D. Exploring a dungeon, but sometimes to open a door you must activate a button by leaving a weapon behind holding it down. But if you run out of ammo you can run back to the previous area and pick up an older weapon (but now what? Go back to town and buy more equipment and try to get a little farther?). And maybe to pick up an item in a treasure room, you have to leave something behind to take its place (Raiders of the Lost Arc style). Could end up with very slow progression after a while.

Idea Four:

Sim. You're managing humanity's first great experimental space-station, when a calamity annihilate's Earth. No more resource rockets are coming, and you don't have enough food/water/energy to keep the station running at full capacity anymore. You have to choose which sections to power down, and which (if any) research projects to continue providing resources for. Wait, isn't this just Frostpunk in space?

Idea Five:

Story. Choose your own adventure style. Given several options, make your choice. Some choices require you to give something up, or for others to make sacrifices. Can you get to the good ending? IS there a good ending?! My writer friends would choose this option.