However, there are many video games that have Iyashikei elements. Even the quintessential "save the world epic" Final Fantasy has Iyashikei elements. With FF-VII Cloud Strife playing video games at the Golden Saucer, or FF-XV having a road-trip with bros. Some of the most celebrated parts of the games are Iyashikei, the low-stress parts of the game that were in-between the battle sequences.

Leaving Square/Enix for a second... there's also Nintendo's "Fire Emblem" series. The characters always talk about their personal life. And the player plays matchmaker, trying to get different characters to talk with each other, to discover their personalities. The most recent Fire Emblem: Three Houses, has an entire School-simulator where you set up the curriculum of your students.

Almost all Japanese stories seem to have a part where Iyashikei comes out to destress the main character (and the player).

So the question is, are you interested in games with Iyashikei elements (which IMO, includes almost all Japanese games worth talking about...), or are you interested in games that solely are Iyashikei? The genre exists on a spectrum, from games like Animal Crossing (mostly Iyashikei), to Atelier Sophie (More Iyashikei than not), to Fire Emblem / Final Fantasy ("save the world" epic plot lines, that visit Iyashikei at certain parts of the plot).