You've laid out one potential development cycle: FOSS from the get-go, and open collaboration welcome.

However, that's not the only way that a FOSS game might be developed. The code could be freely licensed, but the upstream developers refuse to accept outside patches. In that case, there's one "original" and then if you don't like it, build your fork.

Alternatively, a game could be developed entirely in-house under proprietary licenses, and then only made FOSS upon commercial release. Contributor patches could improve the project, but conception of the game would be entirely the domain of its original developers.