The relevant passage from the opinion in Torcaso v. Watkins, 367 U.S. 488 (1961) is:
We repeat and again reaffirm that neither a State nor the Federal Government can constitutionally force a person "to profess a belief or disbelief in any religion." Neither can constitutionally pass laws or impose requirements which aid all religions as against nonbelievers, [Footnote 10] and neither can aid those religions based on a belief in the existence of God as against those religions founded on different beliefs. [Footnote 11]
The text of the footnote is:
Among religions in this country which do not teach what would generally be considered a belief in the existence of God are Buddhism, Taoism, Ethical Culture, Secular Humanism and others. See Washington Ethical Society v. District of Columbia, 101 U.S.App.D.C. 371, 249 F.2d 127; Fellowship of Humanity v. County of Alameda, 153 Cal.App.2d 673, 315 P.2d 394; II Encyclopaedia of the Social Sciences 293; 4 Encyclopaedia Britannica (1957 ed.) 325-327; 21 id. at 797; Archer, Faiths Men Live By (2d ed. revised by Purinton), 120-138, 254-313; 1961 World Almanac 695, 712; Year Book of American Churches for 1961, at 29, 47.
This was a case where a man was appointed to the office of Notery Public, but Maryland law required him to declare a belief in God to assume the office. The US Supreme court held that this violated the man's rights under the First Amendment's establishment clause, which had been incorporated against the states by the Fourteenth. The man was not, as far as I can tell, himself a Secular Humanist, and Secular Humanism was mentioned in the footnote merely as an example of a belief system that did not include a belief in God. Why Justice Black used the term "religion" to refer to it, I cannot say, some of the other groups listed in the footnote are clearly religions, and others are belief systems that for First Amendment purposes are often treated similarly to religions.
What might better describe the Court's rulings here than the linked site does is that believers in Secular Humanism, Ethical Culture, and other similar belief systems will have their beliefs protected in just the same way that believers in any religion will. Freedom of Religion includes the right not to have a religion.
By the way, the passage from Everson v. Board of Education, 330 US 1 which is quoted in Torcaso v. Watkins and to which the linked web site probably refers is:
The 'establishment of religion' clause of the First Amendment means at least this: neither a state nor the Federal Government can set up a church. Neither can pass laws which aid one religion, aid all religions, or prefer one religion over another. Neither can force nor influence a person to go to or to remain away from church against his will or force him to profess a belief or disbelief in any religion. No person can be punished for entertaining or professing religious beliefs or disbeliefs, for church attendance or nonattendance. No tax in any amount, large or small, can be levied to support any religious activities or institutions, whatever they may be called, or whatever form they may adopt to teach or practice religion. Neither a state nor the Federal Government can, openly or secretly, participate in the affairs of any religious organizations or groups, and vice versa. In the words of Jefferson, the clause against establishment of religion by law was intended to erect 'a wall of separation between church and State.'
By the way, any site which proclaims that Hugo Black was a "Marxist agent" has lost much credibility in my opinion. Read the linked article and other easily available sources and judge for yourself.