True, the stove itself doesn't produce CO2 directly, but the power plant from which it draws its power probably does.
BTW, they've had welding torches that operate the same way for years. They're more portable than ones that require bulky H2 gas cylinders, which is their intended advantage. They do the same thing this system does: input electrical energy to "unburn" H2O and convert it to H2, then burn the H2 to produce H2O and heat. Since nothing is 100% efficient, the energy available in the form of heat is quite measurably less than the amount that was consumed in electrical power. Again, unless your electricity is not from fossil fuel plants, this is less efficient -- therefore more polluting -- than just using an electric stove.
It's nice that it generates less indoor pollution than gas or wood-burning stoves, but again, the same is true of electric stoves. The pollution is produced at a far-away power plant, not in your home. You still get to breathe some of it, just not as soon.
The suggestion that it would be desirable in areas where electricity is unreliable may have a bit more merit -- it depends how much H2 you can store, I would think. Intermittent electricity could be "buffered" by conversion to H2 and building up a supply, then recharge when electricity is back on. Not sure if the economics of that will make sense, though -- that would be heavily dependent on local conditions.
ETA: That last para -- it's effectively functioning as a UPS* for your stove.
* Uninterruptible Power Supply, for those who haven't seen that TLA** before.
** Three-Letter Acronym