I thought of an idea — a game that involves time travel… … …as a vaguely quantitative (third/fourth, depending on whether the game is 2D or 3D) direction of "movement", rather than as a qualitative Thing That Turns One Location Into Multiple Locations In Story Terms? So, like, when you're playing the game, time moves normally, but you can "scroll" back and forth through time, and the ways in which various objects and locations might change over time are put onto a timeline.
One lot might have a house on it until t, be vacant from t to t + 2 months, 3 days, be under construction from then to t + 9 months, 16 days, and then have a corner store on it from that point on. Maybe there'll be monthly showings of some cult classic movie from t + 8 days to t + 2 years, 11 months, 18 days. Perhaps certain trees will have a height of offset + time since t × rate. Each individual object might just have a few states or vary on one or two axes over time, but the combined result of that would be what would feel a bit like a continuum of time.
Like, for example,
