I disagree with all answers treating the gnat and elephant as allegory for players of varying skill level.
Rather, the actions of the gnat and elephant are the main point. Chess as a game with rules is not very broad. There are only six types of piece. Half the actual number of pieces are identical and have moves that are almost as simple as it is possible to be (with the exception of en passant, and even then, it is not nearly as complicated as many chess teachers and commentators make it out to be). The other pieces are moved in ways so simple a toddler can understand them. The board is a simple square only eight spaces wide. If one only looks from above the surface, chess is indeed narrow enough that a small insect could metaphorically fly across its whole.
However, in the centuries of its play, strategies and tactics have developed almost to excess. There is gambit and counter-gambit and analysis measured in the millions of pages, billions of words spent on dissecting just a few landmark matches together, let alone the game as a whole. If one considers the depth the game can present, it is indeed a sea deep enough to drown the metaphorical elephant in.