Demigods are treated the same as gods. If you look at the list you'll notice people such as legendary heroes or real-life figures that were deified (Antinous or Gwydion for example).

Either they are completely fictional figures whose belief in and/or worship made real ; either - in the case of Antinous - they were real, existing people, but due to post-mortem worship or their divinization, they became god-like entities after their death.

A similar case seems to happen with the New Gods, as in the novel it is noted that they have in their ranks people looking a lot like famous movie stars and such, implying that if you become famous enough in culture you can get a "worship" equating you to a modern form of a god