Blizzard could choose to set it up at either character creation or game creation. There are reasons that I prefer game creation, but others disagree.
If at character creation, FFA-only looters will only play with FFA-only looters (think hardcore/softcore and seasons/non-seasons). If at game creation, the game creator chooses, the game indicates what it is, and all additional players use that loot system. For example, I create a game where I select personal loot as the option. It will list personal loot in the game title (or have it be a selectable option) when looking for public games (e.g. think of D3 where yo can select key warden, bounties, regular rifts or greater rifts).