They remind me of magic devices, introduced when leaded gas was becoming rare, that were supposed to enable an old engine to run OK on unleaded! Difficult to imagine anyone today would fall for that. Looks like you have a couple of souvenirs you can use at parties, for a guessing game to pass time!
Interesting to see if anyone comes up with the real answer!
Actually those do keep the fuel fresh. As far as hp gains I've never seen that. I dropped one into a 5 gallon can of real old gas (2+ yrs) and it brought the gas back to normal. I had about 35 gal of gas that was purchased for my generator during hurricane Charlie cleanup. In the mess I forgot about the cans gas stored in one of my out buildings. Anyway it will preserve gas or bring back fuel that has aged poorly.