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It doesn't precisely match Rogue, so it can't be a roguelike!
To be fair, Phantom Eden does seem to eschew
some traditional roguelike aspects; significant carryover between games (emphasis on
significant; yes, many roguelikes have ghosts, but that's very different from Phantom Eden's, uh, Phantom Eden) is the big Thing That Makes This Game Arguably Not A Roguelike, and the lack of ASCII also contributes.
Still, I'd say that Phantom Eden is pretty much a roguelike. It doesn't perfectly match every aspect of a traditional roguelike... but by that logic, you could say "Well, any game with pre-generated levels isn't a roguelike, since roguelikes are supposed to have randomly-generated levels!", and that would remove pretty much every major roguelike from the category.
It's a bit early to judge, but as a Person Who Has Played Loads of Roguelikes
TM, I'm willing to declare Phantom Eden "probably a roguelike", since it definitely isn't a roguelite. I guess we could bust out "roguelike-like", but even
that seems a bit too far; maybe we should just cut off half of "like", making it a "roguelike-li"? Except that that sounds dumb.
Detocroix: Have you considered adding some kind of "grid overlay" button? Judging distance might be a bit of an issue, otherwise, since the boundaries between tiles aren't clear.