One example could be a game where the story is told in a very flowery and overly poetic way that doesn't really add to the gameplay. Like, every description is a long, drawn - out passage full of words that most players have to look up in the dictionary.
There are also some indie games that try to be too artsy with their stories. They might have a very abstract concept for the story that is not well - explained or seems to be more about making the developers look creative rather than providing an enjoyable experience for the players. For example, a game where the story is just a series of strange, disjointed events that are supposed to be deep and meaningful but end up just being confusing and pretentious.
Some role - playing games might have a pretentious game story. For instance, a game where the backstory of the world is so complex and full of made - up jargon that it's difficult for new players to get into. The story might involve a lot of different factions with overly elaborate names and relationships that seem more for show than for an actual engaging plot. It might be like a game that spends so much time on the lore of its world that it forgets to make the actual story fun and accessible.