Sutra Tantra and Dzogchen are all three different systems. Sutra is the way of renuciation, Tantra of transformation (by transforming the workings of mind) and Dzogchen of direct, spontaneous liberation.
The Nyingma school has Dharma broken down into a 9 yana system:
The Sutra System
1. Shravakayana (Hinayana) the Vehicle of the Listeners or disciples.
2. Pratyekayana (Hinayana) the Vehicle of the Solitary Buddhas, the way of solitary meditation.
3. Bodhisattvayāna (Mahayana) the Great or Causal Vehicle, the Vehicle of Enlightened Beings, is the way of those who seek or attain enlightenment for the sake or intention of liberating not just oneself, but all sentient beings from Saṃsāra.
4. Kriya (Wylie: bya ba'i rgyud) Tantra of Action
5. Carya or Ubhaya (Wylie: u pa'i rgyud or spyod pa'i rgyud) Tantra of Conduct
6. Yogatantra (Wylie: rnal 'byor gyi rgyud) Tantra of Union
7. Mahayoga (Wylie: chen po'i rnal 'byor) Great Yoga
8. Anuyoga (Wylie: rjes su rnal 'byor) Subsequent Yoga
(Wylie: lhag pa'i rnal 'byor or rdzogs chen) Ultimate Yoga; The Great Perfection
There is no separate 10th 'yana' for Dzogchen. In the Sarma traditions there's tantric Mahamudra and sutra Mahamudra. I just assumed that the same goes for the Nyingmas as well, there being a certain amount of symmetry to the systems. So that's why I see what you are calling 'Dzogchen' that isn't tantric as being part of the Sutra path.
In the Tantra of the Beautiful Auspiciousness (bKra shis mdzes ldan gyi rgyud), this "Great Primordial Purity" (spyi gzhi) is defined as follows:
What is known as "The Great Primordial Purity”
Is the state abiding before authentic Buddhas arose
And before impure sentient beings appeared;
It is called the great Primordial radiance of immutable awareness.
Sometimes you can get shown the light
In the strangest of places
If you look at it right.