It's officially supposed to be as non-specific as possible. (It fails at this even when not being hijacked by extremists.)
The only legal defense that even exists for any of the blatant-but-trivial first amendment violations by the government is that they're just "ceremonial deism" and not specifically Christian.
That's what "non-denominational" means in the context. Not containing any ideas specific to any denomination, or even specific to the Abrahamic religions.
It has to be super-duper vague and generalized, because it is literally against the highest law of the land for the government to promote one religion over others
Also, dominionism is a denomination; an subset of a larger religion with distinct beliefs and ingroup identity. Specific churches either are or aren't dominionist.
(And as for actual confusion about what "denomination" means, the churches that literally call themselves "non-denominational" are some of the most isolated, divisive extremest asshats in the whole religion.)