It's not so visible if you can't see glue still on the seam like on that work.One of the tori was cut and reglued around the other. The gluelines are visible on the right hand ring.
I disagree about not having enough space to free the rings when carving. I've carved a chain and had less space than that.Wood carving a chain is a fairly old technique and if you google "wood carving a chain" or visit a local wood carving club you can see how it is done. The links are always elongated (just like a real steel chain) such that the individual links can be separated from each other and the grain orientation will be 90 degrees off on consecutive links. The rings in the photo have identical grain orientation and there in not enough difference in size of the hole and the size of the ring to allow them to have been carved/separated from one piece of wood. The most likely way to accomplish that as far as I can see is that one ring must have been broken and glued back together around the other one. Back in the 1970s I made chain using the standard technique where you start with a square length of wood, cut the corners out so the piece has a cross section like a + sign.
Yes. I may be wrong and I understand that it could be carved but it looks to me like a pair of gluelines.