Well, it would be a very dark turn for the fanfic. The Asgardians who were left would be in even more chaos without Thor. His death could have led to the total destruction of Asgard's remaining people, as they didn't have their king. And on Earth, Iron Man and the others would have had to face Thanos with even less hope. They would have to find new ways to combat Thanos' power without Thor's lightning and brute force. It could also lead to some characters like Captain America doubting themselves more, as they lost such a strong ally.
In this kind of fanfic scenario, the entire plot of the MCU could have been drastically different. For example, the remaining Avengers would have lost one of their most powerful members. Thor's strength and his ability to wield Stormbreaker were crucial in the actual Infinity War. Without him, the battle against Thanos on Wakanda might have been a total disaster much sooner. His death could have also deeply affected the morale of the other heroes, perhaps leading to different alliances and strategies that we didn't see in the original storyline.
If Thor died instead in Infinity War, Valkyrie might have stepped up more in the story. She could have been motivated by Thor's death to take a more active role in the fight against Thanos. Also, Loki might have had a different reaction. Maybe he would have been more vengeful or tried to make a more drastic move against Thanos. And the Guardians of the Galaxy might not have had the same connection to the events on Earth, since Thor's presence was part of what brought them into the main conflict.