re-imagining (god I hate that term): game using an existing franchise but wiping the canon clean, plotline and possibly gameplay have a striking similarity but gameplay scenarios are different
Does that about cover it?
Not really, that description can be applied to many sequels (which you didn't define btw) that wouldn't be called "re-imagining". Example - most any Nintendo game. I guess you could go out on a limb and say every Zelda and Mario game is a "re-imagining" of the original, but I'm not sure that would hold much weight.
Not bashing you here or anything, I'm just more confused about remakes, sequels, and "re-imaginings" than I was 12 hours ago.