How can a waterproofing material be "water-based"?
One might need to have more information about the product you've posted to say what occurs in the specific example. But, the general concept could be similar to Latex (water-based) paint. Where the water proofing chemical is dispersed by an emulsion, and once the water evaporates, the proofing material is restructured by its, now unhindered, intermolecular forces. These forces might be strong enough, once the proper structure exists, to resist water coming back and trying to interrupt the interactions.

Below is the Wikipedia explanation for my example of latex paint.


  The term "latex" in the context of paint in the USA simply means an aqueous dispersion; latex rubber from the rubber tree is not an ingredient. These dispersions are prepared by emulsion polymerization. Such paints cure by a process called coalescence where first the water, and then the trace, or coalescing, solvent, evaporate and draw together and soften the binder particles and fuse them together into irreversibly bound networked structures, so that the paint cannot redissolve in the solvent/water that originally carried it.