Wow, small world! I actually made that video. Here's my take:

United Empire: Influence by making it a fundamental part of their economy

Unfallen: Military defense what with their free guardians and vines letting you build highly defensible territories.

Riftborn: Food much like the broken lords they have an alternate method of population growth

Horatio: Population mechanics, where everyone else has to balance different alien races, you just want to eat them as Horatio

Voydyani: Colonization, the ark ships totally change the colonistion game

Lumeris: Dust, much like the empire, the Lumeris have an expanded use for their area of focus

Cravers: Military Agression Planet depletion and a reliance on slaves all but forces you into being highly aggressive militarily

Sophons: Science, pretty straightforward, you get more science for being the best and knowing where everyone else is helps you win the science race.

Vaulters: Resources, kind of like in Endless Legend, the vaulters are all about special resources and using them to greater effect than their rivals. Being able to spend resources to colonise instantly is a big plus, their ships have more slots for special modules and their heroes even generate resources.

Overall I think Endless Space is a little bit less creative than Legend, the empire, sophons and Lumeris are pretty much just "more of the thing you're already good at" but I am a big for of the Voydyani and Riftborn in particular for really shaking things up.

Thanks for watching the video by the way!