Hmm.... my ideal game... let's see. I'd make it an RPG, playable in 3rd, or 1st person, with a Perk system similar to Fallout, set just days before an apocalyptic event. Let's say Zombies, and other assorted nasties, like Resident Evil style. Using a system similar to Bethesda games of time advancement, except things happen while time is advancing. You need to eat, sleep, drink and survive. I would make every building explorable, but hand-craft each location rather than using procedural generation.
Guns would need repair, but not a silly amount like in Fallout or similar games, but a more realistic feel. Bullets would be abundandent at first, but then grow scarce, and soon become currency, while the dollar is still money at the beginning. Society changes as time advances, society breaks down, chaos, then societal revolution, of which you can either join a community that will spring up, start one, or go it alone. This community can be influenced to behave in certain ways, depending on player actions, but this won't be the focus of the game, rather a component that is optional.
The simple idea would be to survive, the game would have no real ending. No game over, and there would be a main mission, but it could be ignored, but not in a Skyrim ignored fashion. Rather, the main mission isn't obvious, in fact, you may never discover it. It will never pop up, it won't direct you to it. It could be as simple as finding a note somewhere in some home pointing to the virus origin.
This supposed Apocalypse could even be prevented by you, the player, if you act fast enough at the beginning of the game and don't use things like resting a lot, which would advance time and date. You could have a full game experience without the Apocalypse as you tried to avert it, in some fashion. There would be an initial selection of professions, which would determine your starting home, equipment, currency (Usable as standard at the beginning of the game since this starts days or a week before the Event), and vehicles. I would make the game an extremely large playing area, we're talking possibly an entire state (Or at least section of a state, perhaps a county), hand-crafted, no procedural generation aside from maybe trees here and there.
You could get super abilities via ingesting chemicals that are essentially instant gene-therapy, or not, if you choose. They wouldn't be essential, unlike the Shouts of Skyrim. I would make nothing mandatory, no abilities required by the game, everything would be optional. You don't even need to kill, not even the zombies... avoid them. I would make it so the zombies would have hearing, sight and smell, with different types having different levels. There would be no auto-leveling of the enemies of any sort, the enemies you encounter are entirely dependent on the area you're in, or as a result of your actions. These Zombies could even be controlled by you, the player, if certain conditions are met, and powers acquired. Again, optional.
You could decide to do nothing, and just live out your life in a safehouse. There would even be in-game games, mini-games, or even perhaps one or two sprite-level full-on RPGs or something. Even movies. There would be vehicles, including boats and helicopters, but you'd better have the skill to use it. Ever try to use a boat without the knowledge? It isn't easy.
Food would even decay at least, organic food, meaning you'd need to hunt for food, or grow it yourself. I doubt I'd put in building your own buildings, but a limited form of construction could feasibly exist.
Anyway, that is my idea.