One of my favorite parts of Endless Legend and Endless Space 2 is the quest mechanic. It adds more objectives than just build and dominate. Will there be quests in Humankind? Should there be quests in Humankind?

If there are quests, do you think there should be specific quests for each civilization that you choose?

A bit too fantasy like for my tastes.  I'd prefer that mechanism be confined to the Endless series.  I guess we'll see what the dev team has in mind once they're ready to share more.

From the sound of things, each civ will have specific activities that yield more Fame than if performed by other civs.

That will kind of be your meta-quest; exploit your chosen civ's Fame efficiencies.

I watched the video. It was really interesting. Here's the tl;dr:

Big focus on Events (those one-off things that pop up in ES2)

The Events are inspired by historical events

They happen in a specific context or by a specific trigger

They can be based on a specific city or involve the entire empire

Options will be available

There are immediate effects, but also long term consequences

They can be disabled in the options

Now, the only hint I got about quests was: since there are no distinct factions, there is less of a focus on delivering faction lore. So, we could probably rule out faction quests, but there is still room for minor factions (or their variant) if they exists and world quests (multiplayer quests).

I'm still all for Quests since, IMO, is what makes the Endless games a lot better than the Civ games. 

In addition to the obvious lineage to the 'Quests" in the Endless games, this sounds a bit like the "Events and Decisions" mechanic in the  Europa Universalis game, which represents the semi-random events that can plague or enable your civilization/faction/court.

Certainly there is enormous scope for Random Events in History, and leaving them out of the Civ games was, IMHO, a major mistake for that series ("Events and Decisions" was Modded into Civ V, and it was a great and flavorful Mod)

A great many of the Sub-Narrative Events could be related to other decisions the gamer/AI makes in the game. For example, if your Civ has adopted a religion that started outside your geographical holdings, you could wind up with a Crusade 'Quest' to conquer your 'Holy City' - and all the diplomatic complications that would entail. The schismatic effects of having 'sects' and sub-sets of a religion are also a fruitful source for 'complications', and many of them start out as Random Events - or at least, Events whose origins are so complex or obscure that they might as well be Random in game terms.

Internal Political, Social, Religious 'Movements' have complicated government actions throughout history, and many of them were aggravated by Random Events like specific Leaders or Polemicists: Russia might still have had a Revolution as a result of her dismal performance in WWI, but it would have been a lot different without Karl Marx, Vladimir Lenin and/or Leon Trotsky.

On the other hand, Jason, the Tyrant of Thessaly might have been a second Alexander the Great if he hadn't been hit by a falling pot and abruptly removed from contention. 

Finally, IRL many "Quests" or 'sidebars' in history were generated by the consequences (frequently Unforeseen) of a Civilization/Faction's Actions.  The early Islamic Caliphates hired Turkish mercenaries to supplement their army, and wound up subordinate to Seljik and later Ottoman Turkish Empires, for a particularly egregious example.

As to Minor Factions, they should be a rich source for Random or Semi-Random Sidebars: requests for aid or protection, sources for mercenaries or Trade Goods, sitting on strategic terrain, mass emigration into your borders - they alone could generate enough Quests to keep the average gamer hopping for much of the game . . .