The book "The Chess Companion" (1968) by Irving Chernev contains two of the four stories mentioned in the question: "The Three Sailors Gambit" by Lord Dunsany (which is definitely fantasy), and "Slippery Elm" (which was written by Percival Wilde in 1924, and was reprinted from his collection "Rogues in Clover" 1928). The latter story is a humorous hard boiled detective story in which the antihero enables a man to cheat at chess by passing him the moves written on Slippery Elm pills — there are no science fiction elements in this story).
The story "Slippery Elm" does have a fictitious reference to vitamins. The story (it has 40 pages) revolves around the "Metropolitan Chess Club". It has a member, J. Hampton Hoogestraten, who is intensely annoying to the other members for his vile cigars, for his boasting and for his habit of picking games with weaker players in order to make money off them.
The membership would dearly love to seem him taken down a peg or two. Although the club has strong players who could beat him, it is considered an honour for the best players to even play you. They want Hoogestraten to be humiliated by losing to the weakest player (Reynolds) in the club (whom in actuality Hoogestraten can easily beat).
They hire the services of a detective who sets out to fix the chess match (despite knowing nothing at all about chess). Hoogestraten is easily convinced to challenge Reynolds. They then set out to put Hoogestraten off balance by spreading rumours that Reynolds is practising and starting to beat other players in the club.
"Study — concentrated study, that's how he does it," he explained. ... He doesn't leave the room for his meals: they're brought to his desk — and they consist of nothing but vitamins".
Had Hoogestraten possessed a sense of humor -- which he did not -- he would have seen through the conspiracy on the instance. Instead he inquired nervously, "Where can you get vitamins?"
"Imported from Scotland," answered O'Niell gravely, "they're small animals like squirrels - only furrier."
Ultimately the match goes ahead. In another room they have a Russian grand master, called Niemzo-Zborowski, who is playing along. The master determines the moves for Reynolds and they are passed to him on slippery elm tablets, which he claims he is eating to counter the effects of Hoogestraten's cigars.
After some initial confusion (Reynolds does not understand the Russian chess notation) Reynolds starts to win, but offers a draw when his victory is clear. Hoogestraten is told that he will now be moved to the bottom of the club's rankings since he challenged Reynolds and did not win. Rather than be published in the year book at the very bottom he resigns from the club.
So it is unlikely to be the right answer either, but between these two books you have all four of the stories that you mentioned.