I think the meaning of roguelike has evolved beyond being a game like rogue. After all, a dungeon crawler that's not procedurally generated and doesn't have permadeath would be more like Rogue but it wouldn't be considered a roguelike. I wish the genre of "procedural run-based game with permadeath" had a better name. It reminds me of how shooters in the 90s were called Doom-clones. Platform fighters went through the same phase with "smash clones" for a while. I think the resurgence of roguelikes happened so far after Rogue that players didn't have the feeling of disrespect of their game from the term. Anybody who likes a platform fighter wouldn't want their game reduced to a "smash clone". Same goes for shooters and Doom. But Rogue was far enough out of the public consciousness that "roguelike" didn't feel like a comparison.

What other term could we use? "Random run game"? I've heard "roguelite" to refer to procedural games with progression between runs rather than starting from 0 every time. I also think this distinction isn't very meaningful since I can't imagine many people looking for that style of gameplay loop would be super concerned about the progression system.

Oh boy! God Hand is a comedy beat-em-up as stylish as Devil May Cry 3 and just as hard. You can buy moves with ingame money and map them to various buttons. The results are quite fun.