Wait, are we sure that the Monsters Inc world doesn't take place during the film itself and not after the events of the film?
Tasha Sounart confirmed that the story is original and taking place after the events off the film.
Monster's Inc. world following an original plot
Even Halloween Town from
The Nightmare Before Christmas in both the first and second games largely had an original story with the former taking place before the events of the movie and the latter taking place after the film's events.
Also, I'm still perplexed to know why the majority of you are jumping the gun saying that this world is following the films plot, Pixar had said
(according to Nomura in an interview at D23 2017 regarding the Toy Story world) that the worlds based on their films need to have an original story that are exclusive to
KH and fit somewhere within the film's timeline
(e.g. Toy Box story taking place between the events of Toy Story 2 and Toy Story 3), instead of retelling the film's plot with Sora, Donald and Goofy there. I would like to point out a few things here that the story for the Monsters Inc. world is not retelling the plot of the film:
1. When Sulley and Mike Wazowski first met Boo
(sans Costume), the former at the factory and the latter at the restaurant both of them were initially scared of her until they warm up to her once they reach their apartment
[video=youtube;CKsAhkVxd1A]https://www.youtube.com/watch?v=CKsAhkVxd1A[/video]
2. Boo largely remained in her Monster Costume throughout the film until the film's climax where they try to trick Mr. Waternoose.
3. I doubt this is before the event's of the epilogue because Boo's door was shredded by the CDA so that she will never invade the Monster World again. It wasn't until by the end of the movie that Mike had to rebuild Boo's Door with Sulley putting in the missing piece that wasn't shredded and he was reunited with her, which is where the event's of the Monster's Inc. story in
III will begin.
[video=youtube;92UI5bpG8oc?t=2m42s]https://www.youtube.com/watch?v=92UI5bpG8oc?t=2m42s[/video]