I think you just click and drag while in the view shown in your first screen grab. As you drag each tab closer to another, you can "attach" them to the side or bottom edge to determine whether they become a child or a sibling. That's how it worked in an early version of NOF that I tried once and your tab view looks identical to that. To me, it seems like an odd way of devising a server structure.
One small piece of advice: It's usually easier to manage a flatter server structure, so only start making sub-folders if you have a compelling reason, not just for the sake of it. It makes shorter URLs too.