A game I’ve enjoyed recently is Avalon, a social deduction game. I would say the main loop that occurs throughout the game is the round format. You debate and discuss who you think is trustworthy, elect people to go on the quest, and vote. Then, the players either pass or fail the quest. I would argue that the architecture of this game is very strongly loop based. However, there are some narrative elements incorporated into the game that create an arc. For example, there are two teams, good and evil. The game determines whether good or evil wins, creating a narrative and lore behind the loops you are playing through.
