HyperRogue - $2.99 USD; A roguelike using an interesting terrain mechanic. It takes place on the hyperbolic plane. A high score chase. Collect treasure from many different realms (all of them are pretty crazy really, with their own rulesets. No real instructions), and the more you collect the more dangers that pop up. Games can take a bit for me, 30 minutes to an hour if I’m focused on it. Otherwise, 10-15 minutes. I really like this one - the lone dev did a great job on the translation. I’d recommend looking for gameplay to be sure it meets your requirements.
Pathos: Nethack Codex - Free: Roguelike in the Nethack vein. Really designed for mobile, touch controls are spot on. Graphics are a bit wonky, so I’d recommend looking it up to be sur it’ll work for you. There is a solid quick save option in the menu, as well as save and quit within easy reach. This one is a lot more involved - it’s a nethack clone almost. I haven’t made it very far, but still good. EDIT: there’s a faux ascii option that’s much clearer to read and decipher.
There’s also Pixel dungeon and Imbrogilio. I don’t really recommend the former since it hasn’t been touched for ~2 years now. iNethack 2 is actual nethack (3.4.3) but it’s ability to be one handed and easy to read is very suspect.
I’ll dig through my games and see if there’s anything else that pops up tomorrow.