The prisoners' dilemma is one of a whole class of thought experiment "games" that are defined by the structure of the payoff matrix. These games are generally framed in terms of two or more "players" making simultaneous choices.
In that context, not being able to objectively see the choice made by other players making their own choice is functionally equivalent to making simultaneous choices. You can re-order when the players make choices and communicate at will without changing the payoff matrix and mathematical model.
In that context, not being able to objectively see the choice made by other players making their own choice is functionally equivalent to making simultaneous choices. You can re-order when the players make choices and communicate at will without changing the payoff matrix and mathematical model.