Since this is a safety topic, I thought I'd copy my YT comment here as well:
Chemistry:
Chlorine in tapwater is either dissolved chlorine gas (which is in equilibrium with similar forms, like hypochlorite, depending on the pH), or chloramine (the nasty stuff you get if you clean a toilet (urea, ammonia) with chlorine based disinfectant -- don't do it!).
In either case, heat decomposes both of them into harmless chloride (e.g., salt), and either free oxygen, or chlorate (which is a beefier version of chloride -- not particularly healthy but less toxic than hypochlorite).
These devices are remarkably effective, and chemically safe:
Line frequency oscillates fast enough that any electrolysis reaction is quickly reversed, so there is little if any erosion of the electrodes (which would break down the stainless steel electrodes, releasing iron, chromium and nickel), nor generation of gas.
The gas bubbles observed should be almost entirely from dissolved gasses (mostly CO2 and oxygen), with a very small amount of liberated hydrogen and oxygen.
The obvious drawback: the average potential in your mug of water is half the mains voltage, and for you blokes that's worth a full jolt of US mains!
There's also the complete lack of power control, which still might be fine if you just need to warm some water for washing up (or maybe making tea, but I still wouldn't recommend drinking it), but just isn't wise for anything dissolved in there. (Anyway, even with the AC input, I wouldn't count on your cup of hot chocolate escaping without a distinctly metallic taste.)
Tim