Personally, I would say it's closer to: (items in parentheses are known attributes of the Planetfall factions)
Vanguard -> Warlord (unit production cost reduction doctrine, no war reputation penalty doctrine, and relatively straightforward units)
Amazon -> Archdruid (fairly analogous to 'Elves' of the prior games, though, I admit, but anyway: utilizes flora and fauna, forest-related effects, terraforming of some sort, high mobility)
Dvar -> Dreadnought (and yes, Dwarves: heavily mechanized and armored, lots of explosive area damage, and mountain-related effects)
Syndicate -> Rogue (stealth, flanking, npc-faction diplomatic bonuses, mind control)
Assembly -> Necromancer (Cyborg being non-Mechanical and non-Biological, but sharing some aspects of both, is similar to 'Ghoul'/Undead... and some of them look kind of like Necrons)
Kir'Ko -> Sorcerer-ish/Warlord-ish (this one is a bit of a stretch, but they have more esoteric powers combined with several very directly attacking units, also they are the only truly inhuman faction)
If also touching on the Secret Techs, then hmm...:
Promethean -> Dreadnought (mechanized, flamethrowers, anti-Psionic/Biochemical)
Celestian -> Theocrat ('holy' theme, 'Enlightened' functions similarly to Devout)
Xenoplague -> [Unsure/Archdruid] (limited knowledge outside of genetics research lore, Biochemical damage, a unit which can spawn sporelings, and the Parasitic Symbiosis unit mod)
VoidTech -> Sorcerer(?) (weird esoteric technology, including Void Blades and Gravity Bombs)
Psynumbra -> Sorcerer(?) (extra-planar origin for units and powers)
"-sis" -> [Unsure] (they appear to have an A.I. theme)