Virtually means "almost (in respect to degree or strength)" or "almost completely".
In your first pair, the difference is very small:
This mission is almost impossible to achieve.
This mission is virtually impossible to achieve.
Here, I think virtually is a stronger choice, so the second sentence simply means the mission is more difficult than the first. Both sentences mean basically the same thing.
Your second pair has a much bigger difference:
He was almost killed in that accident.
He was virtually killed in that accident.
Here, the first sentence can mean either:
He was almost hurt in an accident, but he wasn't hurt at all. (For example, his car almost fell off a cliff, but it didn't fall. He got out safely.)
He was hurt very badly in an accident. He almost died from his injuries.
On the other hand, the second sentence (with virtually) can mean only the second sense. He was hurt badly and was close to dying.
Perhaps a good rule is to imagine that the adjective modified by virtually really is true, but then take a tiny step back:
He was killed in that accident. He's dead.
He was virtually killed in that accident. He's been in the hospital for a month.
"To inaugurate" is fairly archaic in American English. We say people get inaugurated in political office, or to inaugurate a new policy. I couldn't tell you exactly what the difference is, but I can't remember the last time I heard someone use the word for anything but a new president.
To say something "launched" implies movement, and a certain element of risk. Its usage is metaphoric, as literally speaking only vessels launch. When you "launch" a new software, you are taking it from its safe harbor (the development team) and putting it out into the dangerous seas (the general public). It used to imply adventure and risk, but is now sufficiently commonplace that people don't normally think of it that way. "Released" is a more neutral word for the same thing.
Best Answer
Particularly in role playing games or any game that takes place in a made up universe, the lore typically refers more to the backstory/history of either your character or the game world, while the story refers more to the current events of the game and the various exploits your character undergoes.
For example, in the Halo franchise, the different missions you go on in Halo 3 – the narrative given around them, the dialog among characters during those missions, the cutscenes that take place and such – all comprise the story of that game's campaign. But the broader picture of why you're doing that stuff, and the backstory around, for example, how it is that the Master Chief is so much taller and stronger than all the other humans, is all part of the game's lore. Some of that lore is explained through the narrative of the first two Halo games and opening cutscene(s) of Halo 3, and some of it comes from what you actually did as part of the campaign in those past games – which is to say that yesterday's story is part of today's lore.
This can be kind of confusing because "story" could be considered a synonym for "lore," but I suspect this is the distinction your friend was trying to draw.
So if some game has good lore but "not much attention has been given to the story," that may mean that lots of quality past updates have contributed to a rich history around the game universe, but recent updates haven't contributed to that history much (or at all). For example, in an RPG, maybe a recent slew of updates all focused on balancing, quality of life improvements, and adding new boss monsters to fight so players have fresh, challenging content, but no quests that advance existing storylines and expand on the game's backstory have been recently released.