I have a background in chemistry, but nothing more specific than that.
However, it is the chemistry of the thermodynamics that is the issue here. The internal energy of a system depends on what the substances are as well as their state. The internal energy of 1 kg of water at ambient is very different to the internal energy of 1 kg of hydrogen and oxygen gases.
Burning hydrogen produces energy; that is why we want the hydrogen.
2H2 + O2 ---> 2H2O + energy
In fact we get 286 kJ for every mole of water. The first law says energy is conserved, so the reverse must require energy - again 286 kJ for every mole of water.
2H2O + energy ---> 2H2 + O2
The paper looks like it is going via aluminium, but you still need to put the energy in. Making the aluminium in the first place requires a lot of energy, and also generates a lot of waste.
bauxite + NaOH + some energy -> Al2O3 +
red mud
2AL2O3 + huge energy -> 6Al + 3O2
3H2O + 2Al -> Al2O3 + 3H2 + little energy
Hydrogen burns cleanly, so may well be a good fuel for cars, and you could generate it from solar power, so it does have a role as an environmental fuel, but it is not going to solve the energy crisis. It is more like a battery; an energy store.
Of course, if you get fusion working, then it is a fuel for that, but that is a very different thing.