What happens during the fermentation process of the eco-enzyme?
The recipe is using yeast to convert the sugar into alcohol (ethanol). All of the proposed cleaning effect is from the dilute alcohol (and also some vinegar).  The citrus peel provides some aromatic oils. There may be low levels of some particularly hardy enzymes released from the rotting fruit and dying microbes, but it is difficult to imagine that any of those proteins have any effect on removing dirt from clothes, dishes, or surfaces. The solution is also acidic from the fermentation and the dissolved CO2 gas--just like if you used grape pulp and skins you would make a primitive wine with this recipe, and that wine would then turn into vinegar (acetic acid, HOAc).  Mixing some vinegar and alcohol would give you the same cleanser.

The enzyme concentration should be similar to the amount of active enzymes present in homemade beer or wine--would you use either of those for cleaning?