It's fair to assume that each roll of the die is Abed playing out each scenario in his head. Each moment is exactly what would happen when every person's number came up as Abed is a great student of the group's character. Abed knows Annie would get herself a gun because he knows she lives in a bad neighborhood. He knew Pierce would be jealous of Troy moving in with him and would try to get back at him, and, presumably, Troy told Abed about the Norwegian troll watching Troy sleep. Crosses into Fridge Brilliance.
The effects of whoever leaves to get the pizza are implied to represent what would happen if that person left the group for good. Or is it meant to represent what would happen if that person became The Leader? (Pierce's timeline has the most Ship Tease, Abed's timeline has everyone getting over-emotional and arguing with each other, Troy's timeline ends in disaster, etc.) Why else, Jeff's timeline is the one with the Happy Ending.
Everyone Is Jesus in Purgatory: It's possible to interpret every single timeline as how each member influences the group or what their personality is like. When Abed leaves the room, the group gets overwhelmed by their emotions. When Jeff and Pierce leave the room, the group became more cheerful and united.
Soooo, Troy keeps the chaos away?
Troy's the only one (possibly because he's just too dimwitted) of the group that is genuinely nice to everyone. He gets angry/frustrated like any person, and his choices aren't always entirely selfless or for the best because he's not perfect, but he has no prejudice. Think about it: In the first episode: Pierce hates young people (or all people, or life, or something...), Shirley's ultra-religious, Abed can only see people as tropes which inevitably leads to prejudice, Annie is a little pretentious/thinks she's smarter than all the others, Jeff definitely thinks he's too good for community college and Britta has her high-and-mighty 'look I'm an activist and I care about issues' thing going on.
Harsher in Hindsight: Troy's absence leading to the darkest timeline seems harsher after Donald Glover left the show in the fifth season, which became the last season after NBC cancelled the show. You could say Troy leaving the group really did lead to the darkest timeline. This was later subverted when it was announced that Yahoo! Screen would produce at least one more season with virtually the same budget as the NBC seasons.
Jeff, for using a six-sided die in a group of seven people to determine who has to go get pizza, meaning he'll never have to go to get pizza. Abed calls him out on it in the real timeline.
Abed also may count as this, seeing as how he sent a fake club invitation to Jeff a month ahead, just so he would keep his calendar open for the party.
Memetic Mutation: The moment where an oblivious, smiling Troy comes back to find the apartment has become a flaming warzone in under two minutes. The clip of him entering the apartment and stopping dead in his tracks as he surveys the pandemonium is frequently used as a gif in reaction to both fictional and real-world events, usually when a situation has suddenly become very dramatic. It's particularly common on social media like Tumblr and Twitter, where someone can leave their feed for a given period of time (say, to go to sleep) only to return to find that everyone they're following has suddenly gone crazy over something.