Yeah, I think you kind of hit the problem that people have with this paper, namely, how does Li exist un-ionized on both sides of the battery. They have a figure that shows that based on the amount of S they have in the battery, they can discharge like 9000x the amount of sulfur available to react, which is their basis for saying that it remains unreacted. There could be a multistep process, some sort of odd structure could be forming, but I don't think anyone knows yet, which is why it's both interesting and a little confusing.