Soy milk provides very little soy isoflavones which is what helps with the hormones. It provides proteins and vitamins and other good nutrients, but soy milk and much of the soy added to commercial foods (burgers, etc.) have had the isoflavones stripped from them, as well as much of the nutrients.
If you're looking to supplement with soy, you need isoflavones which are found in tofu, and pill form, and other less processed forms.
As the article stipulate, Oriental women tend to get about 200 mg of soy per day from various sources. The FDA recommends between 50 mg and most of what I read from medical practitioners suggested 70 mg is most effective. But again, it is soy isoflavones that make the difference in hormone, not soy protein. (I delve into this difference a little more my Soy and PMS Symptoms article).
One of the sources I cited for this article, though, I know lists several forms of isoflavone-rich soy, so check those out. You can pick it up as a vitamin supplement in a pill form from most natural food stores.