Yeah, I think we can consider a game to have done it much better if the play manages to express the theme of the project (isn’t this much of what SB harps on? And why we’re still talking about Dog Days?) but like other pop art games are designed to fulfill their form’s demands first. A strategy game must be engaging strategy; a shootman must have good shoots (and really Dog Days doesn’t trip over itself in this regard, it manages to make ridiculous nailguns feel appropriately ridiculous and thus aesthetically appropriate).
Spore is a grand example of Will Wright and his team sacrificing their thematic content (watch & learn about the spread of life (oh and memes == genes)) but retreating under game mechanic demands; the player needed agency and the metaphor immediately imploded.
This argues that thematic expressions are pretty well baked-in to game genres. Shooters are going to lend themselves to tales of power abused, of control; city-sims, by acknowledging the presence of government and its ability to solve problems are inherently left-wing in a modern American context.
Creating new meanings in existing genres, then, can only come from mechanical shifts – and so we get expansive games when they chart new mechanical/genre territory: Stanley Parable, Kentucky Route Zero, etc.