The mechanics are the abstract means by which the game works. The metaphor is the game’s beautiful lie, the fiction that gives the game context and a broader meaning.
The game mechanic is the part of a game that separates it from a book, a movie, a photograph or even a conversation.
All told, if a designer has to pick one or the other, more games can find success with a weak theme and a strong mechanical core. Whereas games with an incredibly cool theme but weak or boring mechanics very rarely stick around for long.
Jumping between mechanic and thematic lenses helps keep the game’s design process fresh.