Mmm. Maybe. But it just looks like regular dowels, and said with holes in them, and you can see the lines holding stuff together. The coverings sound a whole lot like regular dropcloths, actually. So, could be you could head to HD, grab those parts and some paracord and cotter pins to hold the lines taut, and just have at it. Because, even if I turned out to be wrong about that - it's what, $20-$30 bucks to do the experiment? Might not be the finished product you'd want to give to a little kid, but if it worked? maybe got to v2.0. and play around the some better hardware.
Alternatively, that frame for the big geodesic dome was just plain dowels and the fittings were actually flexible plastic tubing, like PEX. Three short lengths, stapled or grometted together in the middle. You just spread the tubes out with your hands, and as the structure starts rising, the (ta-dah!) tensegrity keeps all the tubes at the proper angles. So easy, you could put up a big dome alone, just slower that way. But cheap to build, if you already have a parachute laying around, and probably even cheaper, if you wanted to make something smaller.. That was big enough to hold maybe 15-20 people very comfortably? Big enough that he guy who owed it (a photog) could show his work inside with room to spare, anyway.
Reminds me of tents, really. You know, the dome tents with the fiberglass poles? The fittings that hold the poles together are exactly like collapsible fishing rods. So...I guess you could just buy a dome tent - but I'd still roll with the drop cloths, because, if you just wanted a dome tent, you could've bought one in the first place. This one is for playing!