Wikipedia has a decent page on where the term came from and it doesn't mean what Neivert thinks it does. From the page:
There are five forms of eliminationism:[2]
Transformation: deleting/changing the cultural identities of people. (Examples include American Indian boarding schools)
Repression: systematically limiting the power of the target group through political disenfranchisement, ghettos, enslavement, segregation, or other legal means. (Examples include anti-Jewish legislation in pre-war Nazi Germany, Jim Crow laws, voter suppression and Apartheid)
Expulsion: removing the undesired group through deportation, forced removal, forced marches, concentration camps. (Examples include the Armenian genocide and the internment of Japanese Americans.)
Preventing reproduction: forced sterilization, anti-miscegenation laws, or systematic rape so that there will be no future for the group.
Extermination: mass murder or genocide.
https://en.wikipedia.org/wiki/Eliminationism
I guess this total git just got tired of saying "cancel culture" all the time and thought misusing another word would make his whiny book sell better.