Alternatively: The person must challenge everyHorseman to a different game.
A dying man challenges Death to a game of chess in exchange for immortality.
The dying person challenges Death to a game of chess for just enough time to say goodbye.
Death allows the spirit of the unconscious and dying to play him continuously with every victory giving him fifteen extra seconds of life - the longer he lasts the better the chance he will get rescued before he dies.
The dying man is a wizard who has cast a spell forcing Death to engage in this bargain where normally it wouldn't.
Alternatively, Death (for whatever reason) wants the dying man to live a longer life, so he allows it.
Alternatively, Death (via magic) cannot lose any game he is challenged to unless he chooses to, so he allows the souls the illusion of choice. Sometimes, he even lets them win.
It turns out Death just likes to play games.
The dying man has accepted his end, but Death keeps forcing the dying man to play chess.
Death enthusiastically agrees, as he doesn't meet so many people interested in playing chess these days, and even agrees to defer the man's death for regular games.
The dying man has to win his death in order to see the afterlife, compared to the alternative of an eternity playing chess in limbo.
The dying man challenges Death to a game of chess. Death refuses, and takes the dying man anyway.
Death sadly replies that he would love to, but the Celestial Bureaucracy gets on his case when he makes deals like that.
Death asks if he would like to play chess, as it's been ages since anyone challenged him to a game, but is disappointed when the man is too distracted by his recent demise to listen.
The dying man challenges Death to a game of chess. Death refuses. The dying man plays on Death's pride, eventually getting Death to concede to a game.
The dying man challenges Death to a game of chess. Death refuses and suggests a different kind of game.
A dying man challenges Death to a game of chess. Turns out Death doesn't know the rules to chess, meaning the man must explain them as they play. A frustrating experience is had.
Death is not half as intellectual as people imagine, and prefers Snakes and Ladders or Snap!
Alternatively: Instead of chess, the game(s) being challenged is/are games usually considered more silly and trivial than chess, such as Twister, Battleship, Cluedo, Parcheesi, I-Spy, World of Warcraft, Hungry Hungry Hippos, Yu-Gi-Oh!...
Death has played so many games he is a grandmaster on the side. He even held a job at a game manufacturer once.
Building off the "Exaggerated" entry above, the other Horsemen of the Apocalypse challenge the dying man to various other games (playing Stratego or Battleship against War, playing Risk against Conquest, playing Pandemic against Pestilence, and... who knows what kind of game Famine would like?)
The dying man loses the game, but manages to keep avoiding Death through various means. Then, when Death finally catches up with him, the man challenges another game...
Death rejects his offer, as the idea that he plays chess is a myth. However, he will agree to a game of Go...
Averted: There's no mention of a game. Death simply shepherds the soul to the afterlife.
Enforced: "Having the fate of the characters and the world in their battle come down to a game makes for a really tense scene!"
'Is this the part where you challenge me to a game in exchange for your life?, Death asked...'
So, have you actually seenThe Seventh Seal, then? "Um...no, I've just heard about the chess thing..." Oh. I rather enjoyed it.
Due to the popularity of this trope, Death is required to challenge any and all dying people with a game of chess before taking their soul.
I suppose you'll want to play chess for your life, then?
Exploited: People seeking immortality learn to become chess masters. Death is interested enough in facing a good challenge that he allows this to be continued.
Defied: Death informs the recently deceased they cannot challenge him to a game, because too many Chessmasters attained immortality that way.
Discussed: "Seriously, playing chess with Death? You seriously think that's going to do you any good?"
Conversed: "If you could play against Death in exchange for your life, what would you play?"
The dying man's challenge is futile and delusional; Death is a force of nature, inevitable and ruthless. The man loses, and his loss was an inevitable certainty. Death has been doing this for as eternity, and has played and won against much greater minds than this man's.
The dying man challenges Death to a game for his soul and Death agrees. They continue playing for all eternity with occasional wins and losses on both sides but no clear winner in either direction. It is implied that this is the mans afterlife.
Reconstructed: The dying man's challenge is futile and delusional; Death is a force of nature, inevitable and ruthless. The man wins anyway, and Death is impressed enough to give him enough time to accomplish something great.