If you react large amounts of methane and chlorine, the methyl radicals will react with molecular chlorine to make methyl chloride. But if the methane and chlorine are dilute, as they would be here, the methyl radicals with react with something else (like oxygen) first.
Destruction of methane by chlorine has been observed naturally, for example after the Hunga Tonga-Hunga Ha'apai eruption in 2022 (although the chlorine-mediated destruction there was less than methane injected by the volcano itself.)
The link points out that formaldehyde is one product of the methane-Cl reactions. Not sure we're better off with the formaldehyde (and its own further reaction products) than with the methane.
They're not exactly talking about destroying methane. The methane is turning into chlorinated organic compounds.
Formaldehyde is also the product of the natural oxidation of methane by OH radicals.
No, the methane isn't being turned into chlorinated organic compounds. The reaction mechanism is CH4 + Cl --> CH3 + HCl.
(Caveat: I don't think the side reaction CH4 + Cl --> CH3Cl + H occurs, but I need to confirm.) The chlorine ends up as hydrochloric acid, which washes out in rain. If you object to the acidity, note that the electrolysis of seawater was leaving behind the sodium ions as sodium hydroxide, so there would be no net increase in acidity. The methyl radical is also produced by the natural oxidation of methane by OH radicals, and would continue along that natural oxidation chain.
The link I referenced (and the paper it cites) do not, as far as I can tell, discuss any chlorinated organic products.
The methyl radicals will also react directly with the chlorine.
If anyone else is reading along, please do not attempt to use chlorine gas to "destroy" methane in air that anybody's going to be breathing. That would be very dangerous.
I already addressed that point. The chlorine concentration is quite low, so the reactive methyl radicals will react with oxygen first. This is unlike the industrial synthesis of chlorinated derivatives of methane, where methane and chlorine are present at high concentration and oxygen is excluded.
I see what you're saying about dilution. Each methyl radical will run into an O2 much more often than a Cl2. But that doesn't mean the latter doesn't happen at all. There are rate equations and (so far as I can see) you get a long menu of reaction products, at decreasing concentrations.
Even ignoring toxic organics and organochlorides ... the proposal to release chlorine gas seems to demand very careful thought. Similar programs were tried during World War I, with negative effects on human subjects.
Not loving the HCl either, though I've read your comments on that.