The chess scene in The Seventh Seal is arguably the most classic scene in all of cinema:
About a minute earlier the Knight has said that he is not ready and Death told him basically that it doesn't matter and there's no delaying this!.
So why does Death let the game happen?
I assume you ask "why Death allowed Knight to delay his death if he'd told him:
there's no delaying this"
To which my answer is: That's not what Death said.
First, Knight knew that Death had been following him.
Death: I have been for a long time at your side.
Block: This I know.
Second:
Block: Wait a moment.
Death: You all say that. But I give no respite.
Death doesn't give respite. Now for the magic of the movie: Time is non-existent in the movie. Look at how it begins:
there was silence in heaven about the space of half an hour
And just before Death appears, there is silence. Pay attention to how long it lasted (hint: it's about background sounds). Was it for 30 minutes?
Third, Death is seen "personally" being responsible for the death of a person, so we know it didn't have to wait for a person to "die of something".
And fourth: Knight was dead from the beginning. The whole movie is a Dance Macabre, which we are only able to see through the eyes of Jof at the end.
Ingmar Bergman was partially inspired to make The Seventh Seal by a painting by medieval Swedish artist Albertus Pictor which depicts the personification of death playing chess with a knight. As a result Bergman chooses to portray Death as being an enthusiastic player of chess, willing to extend Antonius Block's life seemingly for no other reason than because he enjoys the challenge.
KNIGHT You play chess, don't you? A gleam of interest kindles in DEATH'S eyes. DEATH How did you know that? KNIGHT I have seen it in paintings and heard it sung in ballads. DEATH Yes, in fact I'm quite a good chess player. KNIGHT But you can't be better than I am.
Death agrees to play chess and throughout the game keeps his word not to take the life of the knight, this fact alone already makes the angel of death not the worst character in the film. By the end of the film, there is a feeling that the knight and death are similar:
Both are cunning: the knight offers a game of chess and gets a reprieve from death, and later distracts death with a game and saves the family of actors, and death learns the knight’s plan for the game by cunning.
The knight does not know the answers to many questions, but death also says that he does not have knowledge.
Both are sad from their duties - it seems that both the angel of death and the knight are tired of doing what they are doing, before the start of the game, so to speak - they are both more dead than during the game, both need a game.
There is also a feeling that the knight understands his destiny only while playing, and despite the fact that he loses the game and his life becomes happy at least for a moment when he saves several fellow travelers, without playing with death this would not have happened.
Death seems to have this grim sense of humour throughout the movie, and isn't he kind of known to be willing to prove this point - that you can't escape him by chess or otherwise, you'll always lose.
Playing games with Death has a long history; chess is common, but many other games show up as well. So we would have to look much further back to determine why....
Seventh Seal may be the most famous film use, but such gaming also appears in Bill and Ted's Bogus Journey:
(where Death loses, then demands best of 3, best of 5,...); in The Dove (also Bergman, with the heroine playing badminton); and in the comic xkcd with Dungeons and Dragons.
A large list of other instances in film, literature, etc., is available at [https://tvtropes.org/pmwiki/pmwiki.php/Main/ChessWithDeath]
