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).

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.