Microsoft's PS5 exclusive has a bit of a weird setting but it makes more sense now that the developers explained what it's all about and why everyone is inclined to kill each other.
Deathloop can be either singleplayer or a multiplayer game, where one player is actively trying to prevent the other from progressing. The two players in question assume control of Colt, the protagonist, and Julianna, the other assassin that works to stop him.
All of the plot happens on an island where people are locked in a time loop - the day resets for everyone and there are three main parts of the human portion of this weird ecosystem - wealthy partygoers, Colt and Julianna.
Colt seems to be stuck here against his will and wants to get out by any means necessary. The means, in this case, are killing eight specific targets and he will supposedly be freed of this repeated existence.
His targets are apparently among the partygoers, who see this time anomaly as an unending party with no consequences - everything gets reset at the end of the day, after all. Therefore, none of them want Colt to succeed in his task since it would both mean the end of them and the end of the party.
Julianna jumps in as a new variable. She is another skilled assassin and used to be one of Colt's targets and is now hell-bent on stopping him.
Besides being two assassins stuck in an endless deathmatch thanks to a time loop, their relationship is made even more interesting by spicy barbs they will be sending each other's way. Julianna will taunt Colt from both afar through speakers and even spit vitriol when she's engaged in close quarters combat with him. That said, Colt will not be just taking it silently and he has a few words of his own to shoot out.