The Loch is a 2013 Scottish fishing RPG by Mitch Alexander. In it, you "fight" fish in turn-based JRPG battles symbolizing the experience of fishing. There's a variety of biomes to explore, each with different species of fish to catch, and it all takes place over a series of days with variable weather / variable NPC behaviors based on the weather.
It's pretty rough around the edges, partly due to short development time constraints (it was originally made for a 7 day Fishing Game jam) and partly due to the limitations of reskinning RPG Maker. There's very little tutorializing, and many core interactions don't feel very intuitive. No one really tells you you're supposed to go all the way south to advance to the next day and heal up, or that you have to equip X and then use skill Y to do Z... in this way, it departs a great deal from typical JRPG or RPGMaker game conventions.
But that departure from convention is also refreshing. Though "open world" carries connotations of large expensive 3D worlds, I'd like to expand the bounds of that genre and discuss The Loch as a "small open world" game. What marks an open world game is the repeated traversal of a space, and reflecting on how that space (or the player) changes over time. In this case, the world is a small Scottish lakeside village where everyone speaks in charming accents and encourages you to kick back and slow down.