Other’s have suggested emulating Pokémon. However, if you want a native RPG, the first six Final Fantasy games were remastered for mobile. That’s five whole good games! They all have very frequent auto saving, so they’re pretty easy to just pick up and put down.
These aren’t arcade-y, though. Others have already suggested the best. I like Super Hexagon the most of the suggestions due to its simplicity. Geometry Dash is also great, but sometimes, it just isn’t sightreadable.