The implication (based on the youtube exchange with the author Isaac Arthur below) is that the Amberite civilisation was sufficiently elderly that their sun had long ceased to output sufficient power for their survival as a species. There were also mentions of evidence of a (limited) nuclear conflict.
What seems to have happened is that a small number of Amberites retreated to their moon to conduct biological research and altered their DNA and physiology in order to be able to survive in cryogenic stasis in order to outlive the death of their planet as a life-bearing object.
The motives of these scientists (whether to stay alive long enough to be rescued by an alien species or to serve as a warning to others) haven't yet been revealed.
Enjin: Given that biohazard symbols feature prominently, I'll suggest that isn't an accident. The real mystery is how an extraordinarily lethal biohazard might have between the planet and moon base (one way or the other). If the aliens had time and clear enough minds to "put everything in order", the pathogen most likely was at least slow acting or allowed partial or full resistance to some of the population. If multiple worlds, in separate solar systems have been ended by the same pathogen then it must have been transported. From what little we saw, the moon base seemed to use technology approximately on par with our own, so it's somewhat unlikely that the pathogen was deliberately shared between the worlds (barring some very weird malicious scenarios)...
The easy answer is that the biohazard warnings are unrelated, a red herring and that the worlds were subject to a GRB. The state of Amber being covered in ice might be a coincidental ice age for a world that is often quite cold (as Earth tends to be - not right now of course, we're in a warm patch within a larger cool period, but through the millennia).
Edit: 6 hours later I'm stumped. I can't think of a scenario that fits all of the evidence... unless there was more than one 'great filter'. Multiple worlds, cosmic neighbours that each die due to a biohazard within about a million years of one another, which (directly or indirectly) can freeze a planet and potentially affect the few who escape to a moon base but not severely as they have time to consider their existential crisis and prepare their base for future investigation by an alien species... possibly as a warning of what led to their demise.
Isaac Arthur: You advanced a very solid line of reasoning though Michael :) Though of course I won't confirm or deny any of the options for a while so everyone's had their chance for fun :)
- In reference to the zombie warning(!) signs, these were intended as an easter-egg or some sort of in-universe joke by the scientists rather than a legitimate cause of planetary death.
Isaac Arthur: I will also say, now that someone noticed the text on the sign, which I didn't want to spoil, that the zombies themselves are a bit of a joke, the biohazard symbol however is pertinent to the story.
Isaac Arthur: No Mike, the Zombies are just a joke, that didn't kill them. Of course the biohazard symbol for them would be different. I don't want people getting too sidetracked with that, they were doing bioscience up there, what that is indicating, so folks don't get confused, is that they were very cautious experimenters, to site a bioresearch facility on a moon and still put biohazard symbols on the front door, and that they would have people there who would be experts on biology and DNA so that their last ditch gambit was more plausible.