There are a fair amount of good mobile games that are nonviolent with good, resonant stories. As a bonus, touch controls are usually simple enough to pass back and forth. These games are usually smaller; Apple Arcade is a good way to sample many of them without any free-to-play upselling.

A few nice examples of story-rich games on mobile:

Monument Valley, Assemble with Care, Guildlings, Alba: A Wildlife Adventure, Pilgrims, Mutazione