I don't think he presented enough evidence to make that statement without a lot of qualifiers, but for now, let's just assume that it's correct.
What Piketty absolutely failed to account for is that capitalism's greatest strength (and even Marx thought this) is that it causes the marginal utility of currency to decrease over time.
That means that even if the dollar gap between rich and poor is bigger today than it was 200 years ago, the actual quality of life gap is just getting smaller and smaller.
A billionaire can afford caviar and ten lamborghinis.
A thousand-aire can afford hamburgers and a used civic.
The billionaire is not a million times better off, and every year, as brutal market forces push the development of better and cheaper technology in every field, the difference between the rich man and the poor man, measured in the quality of food, goods, and services they have access to, gets smaller and smaller. For the most part, billionaires can only buy more of the same thing that almost everyone has access to. The rich guy can buy a harvard education, and the poor guy can buy a cheap but effective online education. The rich guy can buy a gold-plated iPhone, and the poor guy can buy a cheap Android. It's all the same stuff, just with different levels of class.
Compare that to not so long ago when only the rich had cars, refrigeration, electricity, etc.