These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Alternate Character Interpretation: In Shogi (a Japanese chess variant), the "king" has also been viewed as representing the children of that player's color — the future, if you will. Referenced in Naruto.
Designated Hero/Designated Villain: The players. The colors for the pieces do not constitute as heroic or villainous traits, so there's no "Hero vs Villain" dynamic unless the players hold a sufficient dislike for one another, and even then, it falls onto perspective instead of narrative.
Ending Fatigue: Some novice games can drag on for quite a while, especially when it's just chasing the king around the board. Professional players would have resigned long ago at this stage. This is the reason why the fifty-move rule was invented (which is still pretty long for an average game).
Face of the Band: Just about anytime chess is referred to, or symbolized, you'll see the Knight.
Nightmare Fuel: Some of the neuroses, pathological behaviors and/or full-fledged psychoses suffered later in life by many historical masters invites the question of just what impact long-term intense study of the game has on the human psyche.
Scrappy Mechanic: Explaining castling to a new player can get pretty daunting. Even in intermediate play a lot of confusion can still occur as to what is or isn't a legal castling scenario.
En Passant can cause a lot of trouble in novice games due to the obscure nature of the rule.
Stop Helping Me!/Surrounded by Idiots: The famous smothered mate where a single knight forces a king into a corner, surrounded by its own "protective" pieces who block out all escape squares, allowing this beautiful (and somewhat embarassing) checkmate. There are countless other checkmates where the King's only escape(s) are blocked by its own pieces, the most common of which (among relative novices) is that of the King being mated by an opposing Queen or Rook on the back rank because he's hemmed in by the three pawns in front of him.
This is also part of why beginning players tend to be cavalier about discarding their pawns: why waste a turn on them when you could be using it to deploy your more powerful pieces? Oh, right: because they're in the way.
Alternate Character Interpretation: Anatoly Sergievsky—troubled Anti-Hero pulled apart by the demands of everyone in his life who eventually decides to stand up for himself? Or a spoiled Jerk Ass whose great success and beautiful family aren't enough, so he abandons the latter, and eventually admits his first obligation is to himself?
The sheer complexity of "Quartet (A Model of Decorum and Tranquility)" is also worth mentioning.
Draco in Leather Pants: Freddie seems to get this a lot from the fanfic writers, but not so much from the rest of the fandom.
See the entry for Alternate Character Interpretation above. The latter interpretation leaves Anatoly as an even bigger a-hole than Freddie, so naturally the fangirls are gonna set about making him even more sympathetic.