No. It's based off of a creepy creepypasta from 4chan. Someone had a vague scary sounding story and put a picture of these yellow rooms onto it and it grew itself from there.

It has nothing what so ever to do with that real world case except for some coincidental similarities. Just because it has a vague reference to something doesn't mean that's what the game is based on.

edit: So both the real world and the game have a person named Timothy King aged 11 who died and ate chicken. That's all of the similarities between the two. Every aspect of the real world case and the game are completely different except for those 3 specific things. How they died, who killed them, why they were killed, how they were found, etc... are all completely different. It's also a Europe based developer so why would they have any connection to the real world case?