Malcolm, I respectfully and earnestly disagree. It literally means "unbiased" or "non-sectarian."
One can still be sectarian and claim to be a
Dzogchenpa, just as one can be sectarian and claim to be a
Chakchenpa/Mahamudrika(?). Rimé isn't a Nyingmapa or Dzogchenpa movement any more than it is exclusive to any other group or practice. Just the opposite; it's inclusive.
Besides, I'm reasonably certain that the three pillars of Rimé---Jamyang Khyentse Wangpo (a Sakyapa), Jamgön Kongtrul Lodrö Thayé (a Kagyupa), and Chokgyur Lingpa (a Nyingmapa)---would all agree that Dzogchen and Mahamudra are different labels for the same state of being and highest truth.
"The Sutras, Tantras, and Philosophical Scriptures are great in number. However life is short, and intelligence is limited, so it's hard to cover them completely. You may know a lot, but if you don't put it into practice, it's like dying of thirst on the shore of a great lake. Likewise, it happens that a common corpse is found in the bed of a great scholar." ~ Karma Chagme དྲིན་ཆེན་རྗེ་བཙུན་བླ་མ་རཱ་ག་ཨ་སྱ་མཁྱེན་ནོ།