The example is a sound one, read more carefully. It says that if PETA is right about meat being MURDER, and they convinced a majority of Americans that was true, then they would have the right to ban meat eating because the majority can ban MURDER. Nope, the example is still bogus, because the author does not require that majority rule shall be limited to cases where this is an issue. Indeed, the author rejects the very notion of principled limits to an extent that makes Bill Clinton look like George Washington.
Protection of minority rights is an exception to the general rule of majority rule.
On the contrary -- in a free republic, "majority rule" is the exception to the general rule of individual liberty.
And besides I think it will be difficult for you to find a fundamental vested right in meat-eating in the constitution.
The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
I guess you didn't read the whole article because near the end he uses an example of certain rights that can't be violated by majority rule, such as choosing one's own religious observance.
"The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people."
Sweet! I guess I have a right to smoke pot and use cocaine because the constitution doesn't say otherwise! It is that same screwy logic that allows liberal judges to read all kinds of "rights" into the constitution.