Are you interested in seeing games put up on mobile fronts? Maybe you might check out Mysterious Castle[mysterious-castle.com].

I caught notice of this game back on the Roguelike Reddit while 7DRLs were underway. The game itself is a small squad based dungeon crawler RPG, seeing you take up to four heroes to battle against other groups of enemies.

While this technically has a save system, I don't see it as that far off from roguelike games - and you could always just play it as a roguelike until such an option is added in.