I would call Hades and pretty much anything people call an “action roguelike” a roguelite, but I have a hard time calling something not a roguelike for using graphics, even being pretty strict about the definition. Like, there are a number of originally-ASCII roguelikes that have tilesets. Those don’t functionally change the game in any way than other than directly dropping the tiles in. Does that mean that Nethack-family games or Dungeon Crawl: Stone Soup aren’t roguelikes?
My red lines are:
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Gotta be turn-based. Maybe I’d accept a purely forced-turn version of a turn-based roguelike, like Mangband.
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At least some element of procedurally-generated maps and loot that alters how one needs to play the game from run to run. I’d definitely call many games that still have many handcrafted maps – Tales of Mag’eyal 2 or Caves of Qud, say – roguelikes.
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At least the option for permadeath, and that that be the primary mode of play. Some Caves of Qud was originally permadeath-only, but added a mode that avoids it.
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Grid-based. Hex grid is fine, like Hoplite.
Those are Berlin Interpretation elements. In addition:
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Top-down view (or functionally-equivalent, like equivalent, like isometric). I wouldn’t call a first-person grid-based game – and there were a lot of 1980s and 1990s RPGs that used that structure – a roguelike.
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Only direct control of one character at a time. I wouldn’t rule out Nethack for indirectly-controlled pets or Caves of Qud for letting one switch which character the player’s “mind” is controlling.
I don’t think that I’d make it a hard requirement, but all good roguelikes that I’ve played involve a lot of analysis and trying to find synergies among character abilities or item or monster or map characteristics, often in nonobvious ways. That’s a big part of the game.
To me it mostly comes down to just three things that give the roguelike experience. There needs to be permadeath, there needs to be some kind of clock (traditionally hunger) that encourages messy solutions and exploration, and the player needs a lot of tools (inventory) to be able to come up with creative solutions to problems. A lot of these action roguelikes are mostly lacking in giving the player a lot of tools and encouraging them to experiment, they are a lot more like build slot machines that are mostly about good physical execution and understanding basic synergies. These games are still fun but not really the same vibe as a classic roguelike. But a realtime roguelike can be done, I’d argue Barony is just that.