At one point in time, I was rather adept at the practice, being a chess champion at school for a year at the age of 15 over 200 players. As off this current time, I would say I am mediocre (1100 rating) at it, because chess is as much of a game of strategy, as much as psychological warfare. If I were to play a game in-real-life, I would progress further to where I am now (playing chess.com), because that is where my main strength lies (to my detriment).
Chess, contrary to many people's belief, is more a game of reaction rather than strategy. It wouldn't matter to which strategy was implemented, plans change, so does motives and by definition ways to accomplish the goal (checkmate). Having a strategy which is set-in-stone is more likely to lose you the game, rather than win. In this regard, moderation is a better policy than zealotry - one must be flexible, adaptive and receptive to the opponents machinations, in order to succeed in the physical aspect of chess.
With regards to the mental aspect of of the game, as mentioned previously its a game of psychological manipulation. If I were to provide examples - eyes darting to the opposite side the board, is much more of a solid defense then an well-placed piece to reinforce a position. Another example would be the act of hesitation - lingering on one piece would make an opponent question your motives and by extension adapt accordingly. In doing so, doubt is his worst enemy at the moment, which you could compound on by delaying your plan with time. The possibilities are endless and the ways you could exploit that, in the millions.
A few deductions from this: If one were to be a natural master at the psychological aspect of it, they would by nature be great actors. If one were to be a master of the practical at it, they would be very much in-tune with their environment, which confirms what
@brightflashes was saying with regards to ISTP's being good at the game.
To master chess, one must master both aspects of the above. Apologies for the ramble - I have a passion for the game (when everything falls to plan of course).