I am not sure on this. Yes, adding nitrites can form an artificial smoke ring. But a smoke ring is produced by wood smoke too! I believe your electric Cookshack statement, 1st time I have ever heard it. You are sure that smoke was being produced?
I think if you take 3 briskets, rub one with say TQ and cook in an electric oven it will have a "ring" that looks artificial to me, but most would say smoke ring, take a 2nd brisket with nothing on it and cook it in a gas oven, it will have no "ring" and take a 3rd with nothing on it and cook with hardwood you will most definitely have a smoke ring.
This is why your Cookshack cooks puzzle me so much!
It is not related at all to smoke. It is some chemical reaction. I don't remember the specifics. I know when I had an electric Cookshack that used wood for flavor in a box over a heating element, it created no smoke ring at all. I remember recommendations to add hardwood lump charcoal in the wood box with the wood to get a smoke ring.