The author of the site seems to be trying to develop a religious perspective which includes Judeo-Christian, Islamic and Taoist elements but the fact that he emphasizes Hebrew/Jewish terminology makes it more reminiscent of the Noachide movement.
Never heard of the Noachides? They are basically non-Jews who accept and follow the (usually Orthodox) Jewish conception of how Gentiles ought to live.
More specifically, if you take the Bible literally, then even before the covenant with the children of Israel at Sinai, God established a covenant with Noah and his descendents (i.e. all human beings). The sign of this covenant was the rainbow. And on God's side He promises not to destroy the world by flood again. ("God gave Noah the rainbow sign/ No more water, the fire next time") But then according to the Bible, man also has obligations to hold up on his end of the deal as well.
And God blessed Noah and his sons, and said to them, "Be fruitful and multiply, and fill the earth. The fear of you and the dread of you shall be upon every beast of the earth, and upon every bird of the air, upon everything that creeps on the ground and all the fish of the sea; into your hand they are delivered. Every moving thing that lives shall be food for you; and as I gave you the green plants, I give you everything. Only you shall not eat flesh with its life, that is, its blood. For your lifeblood I will surely require a reckoning; of every beast I will require it and of man; of every man's brother I will require the life of man. Whoever sheds the blood of man, by man shall his blood be shed; for God made man in his own image. And you, be fruitful and multiply, bring forth abundantly on the earth and multiply in it."
Then God said to Noah and to his sons with him, "Behold, I establish my covenant with you and your descendants after you, and with every living creature that is with you, the birds, the cattle, and every beast of the earth with you, as many as came out of the ark. I establish my covenant with you, that never again shall all flesh be cut off by the waters of a flood, and never again shall there be a flood to destroy the earth."
And God said, "This is the sign of the covenant which I make between me and you and every living creature that is with you, for all future generations: I set my bow in the cloud, and it shall be a sign of the covenant between me and the earth.
Later rabbinical legal reasoning has taken this passage and others to generate a list of 7 commandments (not even a full set of 10) which are binding on Gentiles according to Orthodox Judaism:
1. Avodah zarah - Do not worship false gods.
2. Shefichat damim - Do not murder.
3. Gezel - Do not steal (or kidnap).
4. Gilui arayot - Do not be sexually immoral (forbidden sexual acts are traditionally interpreted to include incest, bestiality, male homosexual sex acts, i.e. sodomy, and adultery.)
5. Birkat Hashem - Do not "bless God" euphemistically referring to blasphemy.
6. Ever min ha-chai - Do not eat any flesh that was torn from the body of a living animal (given to Noah and traditionally interpreted as a prohibition of cruelty towards animals)
7. Dinim - Set up a system of honest, effective courts, police and laws.
According to some Jewish authorities, these commandments can actually be seen as 7 categories of laws, which can be broken down further into 66 commandments (or 30 in another formulation).
When I stop to think about it, it is surprising that there are actually people who are willing to participate in a Noachide movement under these terms. Judaism offers Jews a very rich and detailed set of guidelines for behavior while Gentile spirituality is a more loosely defined afterthought. Noachides believe that Orthodox Judaism is basically true, but choose not to covert. Nevertheless they still structure their own spiritual and ethical life in Jewish terms by following the Noachide path.
I'm not saying that the author of the Hashlamah page is a part of this movement, but just that one reminds me of the other. Both seem to start with the Torah and Jewish terminology and both seem to wrestle against Judaism's particularism by laying out a path for all humanity to follow.
Online book: The Path of the Righteous Gentile
Wikipedia: Noachide Laws
JewishEncyclopedia: Noachian Laws
Chabad-Lubavitch: Jews and Hasidic Gentiles: United to Save America
Rachav's Page: The Seven Laws Become Sixty-Six