Kyriarchy is an extension of the feminist notions of patriarchy originally proposed by Elisabeth Schüssler Fiorenza in 1992. Kyriarchy still focusses on the oppression of women by men, as evidenced by this quote.
The Universalist kyriocentric rhetoric of Euro-American elite men does not simply reinforce the dominance of the male sex, but it legitimates the imperial "White Father" or, in black idiom, the enslaving "Boss-Man" as the universal subject. By implication, any critical theory — be it critical race, feminist, liberationist, or Marxist theory — that articulates gender, class, or race difference as a primary and originary difference masks the complex interstructuring of kyriarchal dominations inscribed in the subject positions of individual wo/men and in the status positions of dominance and subordination between wo/men. It also masks the participation of white elite wo/men, or better "ladies," and of Christian religion in kyriarchal oppression, insofar as both have served as civilizing colonialist conduits of kyriarchal knowledges, values, and culture.
In moving from patriarchy to kyirarchy feminists themselves are showing that patriarchy was a flawed and overly simplistic idea.
Like the feminist notion of The Patriarchy, kyriarchy is unfalsifiable.