PG makes little effort to identify what it means to earn something. Some people consider effort the measure of whether something is earned. Some believe luck should be subtracted from result to get what is earned. Some say you cannot earn the benefits you receive from your genetics. No idea of what it means to earn something is given except for making users happy while "not cheating" (who decides what counts as cheat…
I think we can clearly say that capital gains are not earned. Someone who lays bricks, "earns" their income; someone who's wealth increases as a bricklaying company's value increases, does not. In this sense, it is indeed impossible to "earn" a billion dollars...
No, we can't say that at all, because most businesses are small businesses, owned by the people who run them, and capital gains are the owners' income from running the business.
The money startup founders make, from building something as PG describes, is also capital gains. So again, no, we can't say at all that capital gains are unearned.