It looks like you can commit code to the game by pointing it at a GitHub repository or other methods[1]. I couldn't find documentation on the GitHub integration but here's some people talking about it[2].
public_repo - Grants read/write access to code, commit statuses, collaborators, and deployment statuses for public repositories and organizations. Also required for starring public repositories.
repo - Grants read/write access to code, commit statuses, collaborators, and deployment statuses for public and private repositories and organizations.
Also, I don't think they need write access at all to your repositories, so I think the default no scope would be sufficient
(no scope) - Grants read-only access to public information (includes public user profile info, public repository info, and gists)
Well, by granular I meant on a per-repository basis, ie. so you could grant an application access to only one repo (If anyone from GitHub is reading this...)
As RadioactiveMan said, they have a somewhat undocumented feature where they will sync your screep code with a GitHub repository. The only way to do that with GitHub scopes is to allow full read/write access to your all of your repositories including organizational repos.
Pretty fun. I did experience an EXTREMELY frustrating issue though. I tried multiple times to complete the simulation. However, you really need to hijack the back button or at least the backspace key. Hitting the backspace key without selecting the code editing window immediately navigates you away from the simulation and forces you to start the entire thing over. Extremely frustrating to say the least, and it prevented me from finishing it.