It looks like the journalist misunderstood the nature of Thomas' complaint. A big clue to his meaning appears in the very next paragraph:
‘Today there is much focus on our rights,” Justice Thomas said. “Indeed, I think there is a proliferation of rights.”
The rights in the first ten amendments are specific and enumerated -- and are focused on preventing the government from overstepping the boundaries of its power.
Thomas isn't complaining about that. He's complaining about a "proliferation" of other "rights", ones focused on the presumed entitlement of individuals, ones which are always exercised at the expense of others.
The distinction is obvious in this paragraph:
He gave examples: “It seems that many have come to think that each of us is owed prosperity and a certain standard of living. They’re owed air conditioning, cars, telephones, televisions.”
Good analysis.