What? Yes, the concept of yin and yang seems to apply to hydrogen and oxygen.
Hydrogen appears to be the yin force. The yin force or quality is yielding, feminine. As the first element, it is the "mother" of all other elements. Also, it tends to seek equilibrium with many other compounds. For example, the hydrogenation/dehydrogenation reactions of butene/butane are governed by the equilibrium. Hydrogen "yields" to the association with butane according to the temperature conditions. In general, equilibrium may be significant for reactions involving hydrogen.
Oxygen appears to be the opposite. It is aggressive in most interactions with other elements and compounds. Oxidation reactions tend to proceed to the fully oxidized state, with no significant reverse reaction. You might even say that oxygen is greedy, possessive. Yang is also associated with fire, and oxygen is a critical requirement for fire.
Another part of the yin/yang philosophy is that the combination of yin and yang make a "whole" that is greater than the parts. And so it is with the union of hydrogen and oxygen...water. Without water, life as we know it would not exist.
So what do the dots represent? They represent the entanglement, or bonds, between hydrogen and oxygen in the water molecule, which is the "whole". They might also represent the exceptions to the equilibrium/non-equilibrium generalities stated above.