The term "Game Developer" is quite abstract and have different meanings for referring to a single person or a team.
If the context is a team or a studio, then yes, everybody working in a Game development studio can be considered a game developer.
If the context is within that studio, then when we say developer we refer to an engineer, and yes, in a professional game company it's very common to refer programmers as engineers or developers, so this is wrong: "Would you call a Software Engineer an Engineer? I would not" in that context. We do that quite often in the company.