Perhaps some sort of novelization of the game is called for here? Just like historical fiction, but with chess games. "Oce upon a time a lonely pawn, for reasons left mysterious to it, traveled forward two squares. That pawn thence met a similar looking creature that was brown where it was beautiful ivory in color. The opposing creature scared the lonely pawn, but the pawn was soon joined by a ..."
You get the point.
Only, this method seems even more cumbersome than just giving the moves, even if it does promise to be more entertaining.