Earlier quoted context omitted.
No, the rest of the court found the the excessive punishment protection of the eighth amendment was applied to the states through the Due Process Clause of the 14th Amendment as an essential right and therefore a component of “liberty” as used in the due process clause. Thomas disagrees with this fairly conventional incorporation argument and the idea of the protection as a fundamental right, but feels instead that a…
Note also that corporations are 'people' but not 'citizens' and would likewise be disenfranchised from the protections provided by the bill of rights and the constitution when it came to state law. edit: there seems to be some lawyering about the difference between the meaning of 'people' and 'persons' that I do not understand at this time.
A corporation, is, by definition, a group of people, yes. And those people who make up the group have rights that are protected by the constitution.
Or in other words, a corporation is the plural form of the word 'person', in many situations.