In this context, closed system is term used in statistical mechanics that says that there are quantities (energy and particles) that may not enter or leave the system. So I would read this is 'if we assume that money plays the role of energy in statistical mechanics, what happens'.

I was a theoretical physicist when this paper came out. I remember talking to some econphysicists at the time, though neither of these two. While as a premise, it probably doesn't stand up to much scrutiny, I think the spirit is that even if one makes such a drastic assumption, can one still observe any observable features of actual economic systems.