"Dominionism" is simply an epithet, usually used by Libs and Progs, that means no more than, "(S)He's a Christian and I disagree with him/her." There is not one Christian Reconstructionist person or organization on the lists you posted (and I think you knew that).
By and large this kerfluffle is over a largely pentecostal variety of Dominionism called the Fivefold Ministry...Largely taken out of context from Cruz's old man selling his kid in large pentecostal settings... speaking their language.
Pentecostalism, from the outside looking in seems kinda kooky on it's own, not to mention layering Fivefold theology on top of it... And the Press had a field day stretching that language and setting well beyond its limits.
Literally much ado about nothing, similar to the ways the Amish are taken as wierdos by those who don't understand them. From within the Pentecostal culture, Fivefold language is far from inflammatory, and really rather bland.. Like any other Christian Restructionist theology.
Seriously a MEH... Till trotted out in alarmist nonsense like that exampled in this thread.