short answer, confirmation of your theory is all right here
Yes, Chlorine Dioxide ClO2 is being produced. Chlorite and Chlorine Dioxide are very similar. Chlorite is an ion and Chlorine Dioxide is that ion as a free radical (with an extra electron). As seen in the chart Karsten's answer gave, Chlorine Dioxide has an additional oxidative punch.
Both Chlorite and Chlorine Dioxide are well known and widely used throughout many industries. They are often preferred over other disinfectant compounds when health (such as food or water safety) is a concern. In your case, they are preferred over hypochlorite (bleach) or chlorine because they will not chlorinate like those compounds do, and only work via oxidation. As a bonus, molecular oxygen is left behind when ClO2 is fully reduced.
That's where you went a little off. No Chlorine gas is required to get Chlorine Dioxide from a chlorite solution. Putting Chlorine or a chlorinator like hypochlorite (HClO) into the bottle would defeat the gentle aim of the product: do no harm to fish. Correct me if I'm wrong, but didn't you already spend so much energy getting chlorine out of the tapwater when you filled the tank?
So, you noticed the oxidation of chlorite by chlorine to get chlorine dioxide but didn't find the more applicable method of simple acidification. Probably because you assumed the whole aquarium would have to lower in pH. No, everything is dynamic. You can have tiny pockets of acidity even in your alkaline tank. Pathogens often create acidity. They also join together and hide using biofilm. For both these reasons, chlorite is the right tool for the job.
Chlorite itself will oxidize, but not as strongly as the free radical Chlorine Dioxide.
What likely happens is the chlorite floats around until it encounters acute acidity at which point it can jump up an oxidation level to Chlorine Dioxide which will oxidize any pathogen around, bacteria, virus, or fungus. Pathogens generally require and make acidity. With enough ClO2 the product can even tackle protozoa and multi-cellular pathogens, even ones with glutathione defense. The ClO2 would have to deplete that defense first of course, but as Karsten indicated in his answer, that's not a problem. Chlorine Dioxide is particularly effective against biofilm.
here's a quote from wikipedia, "Chlorine dioxide is also superior to chlorine when operating above pH 7, in the presence of ammonia and amines, and for the control of biofilms in water..." Chlorine dioxide is considered a selective oxidant because it generally spares organic matter. This is why it is preferentially used in the water, food, and medical industries.
So what is the mechanism?
Eventually oxidation of amino acids, and likely cysteine in particular. In larger organisms ClO2 oxidizes GSH to GSSG and leaves it there, generally not oxidizing further. When ClO2 oxidizes, O2 (molecular oxygen) is left behind. O2 being key for most life, especially the kind considered non-pathogenic, like your fish, or the beneficial aerobic microbes in your tank.
Now you might think, "Well this sounds great, Chlorine Dioxide can kill anything!" and you'd be right. Well, technically. Which brings us to Karsten's otherwise excellent answer and its faint aroma of fear-monger or concern-troll.
Sodium Chlorite, the active ingredient (and the active ingredient of "MMS," which Karsten brought up), can indeed oxidize hemoglobin at high enough concentrations. Also, at those concentrations your fish would be long dead. In fact, if you and your fish drank Chlorite solution in increasing concentration/doses your fish would likely die long before your methemoglobin creation became life-threatening. What's the fish equivalent of 'Canary in a coal mine?' Why is that? Just like the canary, they're smaller than you. that's all.
But wait, this product is perfectly safe for the fish, isn't it? Yep.
let's talk concentration.
MaracynOxy contains 4-5% "chlorite solution" as per the SDS.
MMS (infamous "Master Mineral Solution" referenced above) is a 22.8% chlorite solution. (although in fairness it is dosed in drops, a drop being 0.025-0.05mL)
Aquamira water purifier tablets are 5-7% chlorite.
Closys mouthwash is 0.1% or (1000ppm) chlorite.
and here is an SDS for simply chlorite salt
at 5% concentration you have 0.12mg chlorite in 2.4mL dose
.43mL of MMS would be needed. that's 8-10 drops
or 120mL of Closys mouthwash
Karsten is keen to remind us how dangerous chlorite and chlorine dioxide is while supplying examples which contradict this. Chlorine Dioxide is so dangerous that it is preferentially used to disinfect meat in the food industry. He cites a study as evidence chlorite is so bad which concludes chlorite is less toxic than commonly used compounds in personal care products. He cites a very special enzyme unique to some bacteria (all aerobic, I assume) to deconstruct chlorite into harmless Chloride and molecular Oxygen. The implication being humans don't have that special dismutase. Quick question, when GSH (glutathione) reduces ClO2 what is left behind? any wild guesses?
Karsten neglected to remind us not to drink anhydrous ammonia, Hydrogen Peroxide, hand sanatizer, or isopropyl alcohol.
In the study Karsten cites concerning oxidative stress they demonstrate how chlorite depletes glutathione. The study also concludes chlorite has a lower toxicity to mammalian cells than benzalkonium chloride. Yes, chlorite is considered a less toxic oxidant than peroxides, sodium hypochlorite, or BZK. By the way, you are all absorbing BZK when you use many common eyedrops, eardrops, nasal sprays, hand sanitizers, antiseptic spray, wet-wipes, throat lozenges, mouthwash, disinfectant cleaners, and even spermicidal cream.
BZK is (relatively) safely used in all of these products applied on or in the body even though this study showed Chlorite to be less toxic.
BZK is genotoxic (it damages DNA), causes cellular damage, alteration in catalase activity, acetylcholinesterase activity, and lipid peroxidation 10.1016/j.etap.2016.04.016. But sure, BZK doesn't affect glutathione.
Chlorine dioxide is the preferred compound for treating cooking fats and oils.
Why? It does NOT cause lipid oxidation.
It is precisely the presence of glutathione and the mild way in which chlorite and chlorine dioxide oxide GSH which make it effective in killing smaller organisms while leaving bigger ones. A virus doesn't have glutathione. Chlorine dioxide will bust that cysteine or histidine on the virus structure and now the virus is in pieces. Similar things happen to fungus and bacteria and simple multi-celled organisms too. The bigger the organism, the more complex, and the more resources and tools it has to deal with oxidation. This is why the fungus dies but the fish don't. Now if you bought the 16 oz bottle and decided instead of reading the directions you would just dump the whole thing in you would probably get some floating fish.
that brings us to
a medical case of MMS
(chlorite solution) ingestion requiring a hospital visit (cited in Karsten's answer).
In the study they very scientifically tell us the child ingested 'a small amount.' Well, a 'small amount' of a substance dosed in drops isn't small at all. what are we talking, 10mL? 30mL? that's 2.8mg and 8.4mg of chlorite respectively and 66-200 times the usual adult starting dose of 3 drops. What substance that is generally safe at regular doses is ever taken at 66-200 times? Would that substance still be considered safe? A usual 'dose' of water is 8 oz, let's say 250mL. who here has taken 16.5L of water at one time? 50L? Anyone care to imagine what might happen if you did? If a child did so, would the parent take that child to the hospital? I would think so considering that's over 10% the LD50 for water. That child's life may very well be in danger. (LD50 of chlorite can be found in its SDS cited above. it's 284mg/kg in rats. rat to human dose conversion is generally 0.162x in mg/kg, so if the oral LD50 of chlorite for rats is 284mg/kg we get the HED (human equivalent dose) of 46mg/kg of chlorite which for a 60kg human would mean ingestion of 2.76g to achieve LD50. a 30kg 9-10yo child would be half that.)
The whole 16oz bottle of Maracyn Oxy would be 23.65mg of chlorite and if it didn't kill your fish, especially the smaller ones, it would very likely make them sick. By the way, the LC50 to minnows for Chlorine dioxide is 20ppm concentration over 96hrs.
With Chlorine Dioxide you see gentle vital use after gentle vital use, right up until mention of MMS and instantly the compound is transformed into the most caustic and destructive chemical known to man. Curious. And yet the very same outlets decrying Chlorine Dioxide as terribly toxic and dangerous are keen to promote NO, another free radical associated with wild health claims. Go figure!
Does Chlorine Dioxide have legitimate health claims?
I'm not making any here, but clearly many do make such claims, and it isn't all from kooks either. The compound is well researched but the health research is sparse, only beginning to pick up. It stands to reason organisms utilizing oxidative phosphorylation would benefit from readily accessible O2, hypoxia being a driver of disease. And that's in addition to any pathogen-killing (eg in blood) or biofilm dissolving (eg in bowels) action. As always, appropriate concentration and dose are vitally important.
Methylene Blue solves methemoglobin, if anyone is curious. Also happens to be another common active ingredient in aquarium treatment. And another unpatentable compound with seriously wild health claims (backed by research), which I wouldn't recommend you down entire bottles of or even mouthfuls.
and yes, UV would mess with the chlorite, UV is also redundant since the chlorite is doing the disinfection already.
boy this answer needs some more editing! meh.