Most of these lines pair 모이다 with the word for in order to, giving a set phrase for people assembled with a shared aim: we who gathered to understand each other, the many fans who gathered to see the cast, an organisation formed to defend its members' interests. That phrasing sounds like a pledge or a caption rather than chat. Elsewhere it is just people bunched up over there, or the military-style call to break formation and fall in.
Register: formal in the pledge lines, casual elsewhere