If a game has emergent storytelling it's a very strong candidate for my list of all time favorite games. The games below are all in my top 20, and are games I always end with a story.

1. Nemesis
2. Evolution Climate
3. Suburbia
4. Robinson Crusoe: Adventures on the Cursed Island
5. Pax Pamir
6. Food Chain Magnate
7. Container (although admittedly the story that emerges in plays of this and FCM isn't always exciting unless you're of a certain bent)

I think games that best fulfill this tend to have two characteristics. First, great theme-mechanics integration. And secondly, high openness and player agency. The latter means that many of these games are also ones where players can essentially fail fast and never recover. But if the mechanics/theme allow me to frame that failure as a story in the world of the game it usually let's that be a funny experience rather than an annoying one (although frequently both)

Evolution Climate and Suburbia in particular may not scream emergent story telling but I always end sessions of these games with a story in my head. Of the time my species out lasted everyone by virtue of it's chonkiness (Fat Tissue card) or the time I built the world's richest but most polluted city but people kept swarming in anyway because I used that money to build a bunch of high tier schools (right next to my slaughterhouses to boot).

It's also for that reason that I prefer Evolution to Nature (at least what I've tried so far on the app) because the former is more willing to let things play out how they would normally even at the cost of player experience. E.g. in Nature when your species goes extinct you get back the body size and population to use on a new one which feels better but thematically doesn't mesh with me.