No, not only is this legally inaccurate, but logically false as well.
YOU cited that case, you can't then just move on past it. In that case they were convicted of violating 18 U.S.C. § 245(b)(2)(B).
Whoever, whether or not acting under color of law, by force or threat of force willfully injures, intimidates or interferes with, or attempts to injure, intimidate or interfere with--
(2) any person because of his race, color, religion or national origin and because he is or has been--
(B) participating in or enjoying any benefit, service, privilege, program, facility or activity provided or administered by any State or subdivision thereof;
They then claimed that law was unconstitutional:
they claim that § 245(b)(2)(B) represents, at least as applied to them, an improper exercise of congressional power beyond the authority given to the federal government by the Constitution...
This was a specific claim that Congress did not have authority to pass that law, because there was no authority granting them that power. The court, however found that the law fell
comfortably within Congress's powers under the Thirteenth Amendment as that Amendment has authoritatively been interpreted.
This is precisely where the case ran in to the language you provided. They were not charged under the Constitution, they were charged under a federal law passed by the federal legislature....authorized by the Thirteenth Amendment. Precisely what I said earlier.
...it "has never been doubted" that the power granted Congress by the Thirteenth Amendment "includes the power to enact laws . . . operating upon the acts of individuals" ...
The 13th Amendment, itself does not reach private conduct, it authorizes Congress to regulate private conduct.
What other of the "few examples" that you provided would you like to stand on? Prohibition? No, that granted the government authority to enact THE VOLSTEAD ACT, without which there would be no illegal conduct.
Look, again, this is fairly simple. Absent that federal law....are you claiming that they would have been indicted
under the Thirteenth? Of course not, it limits governmental conduct. Yes, it DOES defeat the very fact you claim it doesn't. If the Constitution specifically applies to individual conduct, there would be no need for further legislation. If I broke in to your house I would be charged with violating the 4th, if I murdered you I might be guilty of violating the 6th and not granting you a trial. Follow that logic.