I am doing a writeup of what I have seen in the video, for everyone that missed it. I don't have the video open anymore so this is from memory. No guarantees for accuracy.
So at the start of the video they showed of a bunch of different race-portraits. They were pretty impressive. There was a huge diversity, not only between different categories, like fungoid or mammalian, but also between species of the same category. I was very pleasently surprised that there were far less Anthromorphic animals than I expected in there and they were pretty damn creative. The amount of visual diversity they managed to achieve for something like "living fungy" or "Thing with tentacles" was really really impressive.
Afterwards they loaded a save from a human empire named "United Nations of Earth", which were Fanatic Individualists and Xenophile. I remember that the "Individualist" ethos gave an increasing chance that pops would diversify. I expect that it makes them more likely to switch to a different ethos or adapt themselves genetically or with technology.
In the save they had a small fleet of 2 military ships, one construction ship and one science vessel. The science vessel was set to scan the whole system and plottet itself a course to every planet in the system and started to scan. Meanwhile the presenter started some research, for colonisation and better thrusters I think, and build additional military ships, which automatically joined the existing fleet.
The science ship scanned some planets, discovering the ability to gain research from one planet through a research station and minerals from another planet through a mining station. Afterwards the ship was sent to research an existing precursor artifact. The chance of failure seems to have a baseline of 30%, for the case that the scientists skill is as high as the artifacts difficulty, and would get higher if the scientist was less skilled and lower if the scientist was more skilled, like you would expect. In this case the research failed and the scientist blew himself up with his science vessel. That's supposed to be a catastrophic failure, a "normal" failure would only result in the artifact getting lost without any result.
Afterwards an election took place and another president was elected. The player also got a mission, explaining the presidents campaign promises, and that we would gain influence through fullfilling them. In this case the mission was to build 4 space stations.
Then the fleet, now with 6 ships, got an admiral assigned to it and headed out to a nearby system. They slowly moved to the edge of the system in order to start their warp. The presenter then explained the other ftl-possibilities that we could have access to. Interestingly we got an glowing point in the target-system which, upon hovering over it, told us where the fleet was coming from and when it would arrive. After arrival we met out first alien, which gave us an positive modifier from being xenophile. Interestingly, despite the alien "just" being some sort of spacemonster, we still got a mission to establish contact with it and it got a, most likely temporary, name assigned to it. In this case it was creatively named "Outer". We then attacked the spacemonster and defeated it. It was a bit strange, the monster was said to have 800-something power, while our fleet had a mere 250-power and it was defeated by the fleet without casualties. The spacemonster left some depris after that and the presenter explained how that could be used to gain special technology through reverse-engineering.
While this was going on, there was also an event-chain that started with the leading scientist of the physics department stealing a prototype-science vessel and running away. We also seemingly got a special mission for that event-chain, but the presenter didn't look at it, so we couldn't tell what we were supposed to do about the missing scientist. We did see that we had a significant science-penalty from not having a lead-scientist assigned to the physics department.
Afterwards the presenter mostly showed of the universe and the how the game looked at the start in the observer-mode.
One more interesting thing is that he talked about tile-obstructions on planets and colonisation.
Regarding tile-obstructions: On the homeworld they were mostly standart obstructions, like slums, that could be cleared out for a few ressources and a bit of time. But he did mention that there could be different kinds of obstructions with different behaviour. As examples he gave some sort of plant that would spread to adjacent tiles and that you would need a special research project for in order to fight it. Another one he mentioned was basically a giant hole in the ground, from which some sort of underground species could emerge over time.
Concerning Colonization, he mentioned that it wouldn't be too easy. He said that terraforming planets would be very difficult. Various ways to colonise different planets unsuitable to your race would be to integrate another race into your empire that can colonise that planet, building robots to colonise planets for you and genetically altering your, or other races to be able to colonise different planets