How is a Steam achievement a score? A score is a scalar value not a Boolean one. And arguably it is not part of the game but part of Steam. You won't get Steam achievements of any game if you get it from another store. But using the Store achievement definition, Jeremy's games also qualify because they have Steam achievements (most games on Steam do have the achievements even those that fall outside of your definition of game).
I never said that steam achievements were a score. Please try to read my posts. I thought it would be obvious that they represent a success state. I also note that you ignored the fact that Harvest Moon literally has an ending.
Also, I don’t know why Jeremy’s games qualifying is relevant. I never said they don’t.
If Steam Achievement is not a score, is Harvest Moon not a game then? Same thing about crafting and building games.
And having an ending is not synonymous with a success state or a failure state. I think it's clear that your definition is not a valid one as many games don't fit it
And I don’t know if you’re aware, but a vast amount of Sims players use the game to build and decorate houses and then play out stories in them. The Sims dying is not. A lose condition, but the final page of their story.
Just because many people choose not to engage with the mechanics doesn’t mean they don’t exist.
Further, if you remove the achievements from games they continue being games. GTA without achievements is still a game. Remove the entire XBox and PS trophies system and all their games still remain games.