I think it's useful to draw a bright line around the 'value creation' that PG is referring to, also. It's not just creating chairs, it's aggregating great wealth by 'disrupting' traditional industries. Those traditional industries have workers and shareholders who lose out.
What makes successful startups so profitable is they displace a large and less-efficient system with a small, efficient one. Efficient in terms of human capital, oftentimes: look how few people AirBNB employs directly, yet have a market cap larger than Marriott. The returns on capital its investors have seen is a result of the substitution of capital for labor (in part).
Of course, to the extent that the creation of a marketplace unlocks value, it can create value de novo, rather than shifting wealth from one sector/company to another. But with 'smart' startup founders seeking monopoly rents (cf. Peter Thiel, writing/speaking virtually anywhere), those returns are also concentrated, and will not trickle down to the larger population.
Furthermore, the wealth inequality cryoshon is writing about is not driven by startups, it's driven by a general breakdown in the implicit social contract between capital and labor. As OP notes, Piketty goes into great detail about the historical causes and likely effects, but the tl;dr (and his book is _very_ tl) break down to: when returns on capital are higher than overall economic growth, wealth will tend to aggregate.
As fans of numbers and algorithms, I hope HN readers can appreciate the simple beauty of that formulation. Piketty's suggested policy response is simple: high taxes on aggregated wealth. Which, after reading (~80%, honestly) of his book, I have to agree with.