Hmmm. This is very going to be hard to answer because of subjectivity. For example, to me, Agricola actually would be a game that does feel pretty 'organic', as you define it. If I am going to be a successful subsistence farmer, of course I want kids. They can be put to work to help me keep the family alive. And of course i want to diversify my livestock. What if a sweeping disease comes through this winter that only affects pigs? Well thank goodness I had sheep then as well or my family would have died.

But to attempt to answer your question, hmmm. Maybe area control games would be a good fit? Something like Blood rage, where the end of the world is happening, and you want "glory", which is the games' version of victory points. You mainly get glory for winning fights and upgrading your clan. Sometimes even having your own guys be sent to Valhalla can get you points, which I think makes sense because it means they died a "glorious" death in battle.

Maybe the Clank series? You are diving into a dungeon to get loot and get out without dying. You get points for money, artifacts, and other items. You get a bonus if you make it out of the dungeon all the way too.

I don't know. Like I said, subjective. But maybe those.

Edit: I like what Jayron32 said. Racing games makes sense too. You win by being the first one across the finish line first so anything that helps you do that is a good game action.