I'm not so sure if its bad science or an entry in a competition for the worst English written by a far Eastern author. Or perhaps its both.
The quote in full obtained by googling:
"A. Ecoballs™ increase the degree of alkaline. In the water Ecoballs™ exceed OH, which will react with stain/dirt under saponification (saponification creates surfact-active agent which lifts the dirt away. The Activated water molecule filters easily into the inside of clothing fibre and makes combination between filth and fibre loose. Under the stirring of a washing machine, the filth will be separated from fibre more quickly and will scatter in the water, so as to reach the effect of cleanout. Mineral oxides condition the water by changing its ionic structure. Sodium and potassium oxides dissolve in the water, increasing its alkalinity. I.e the Ecoballs makes the molecule of the water smaller which returns the water to having its brilliant hydrating properties, high solubility and good permeability. This is so that it can remove stains,odours and provide you with an antibacterial effect. Inside each laundry ball are solid washing pellets. The pellets contain non-toxic mineral oxides."
I suppose its true that as solution gets more alkaline, the more water molecules are converted to smaller hydroxide ions,
But if thats how these things work you could get the same effect by adding a pinch of sodium hydroxide to your wash. Not too much though as your clothes would soon start to rot.