To be honest, what would having that many members do? I dont think the amount of members would make any difference like making the game more well known, specially if some people are just doing you a favor, unless those people you know are hardcore doom/doom-clone fans, in which case I can see them liking this game.
Personally I would make it a public group. The game has a small enough following so that it wouldnt attract annoying users, and if they do they would be just a handful which would be easy to clean up.