It's important to note that the numbers discussed by the New York Times were only of VC-funded tech companies founded this century. There are at least a few thousand private companies in the US worth 1 billion or more. Forbes keeps track of a few hundred here http://www.forbes.com/largest-private-companies/list/ with the lowest on the list having over 2 billion in revenue.
It's nearly impossible to start a company and have it worth a billion dollars within a decade. But if you drop the get rich quick thinking of Silicon Valley, it's much more possible if you grow slow and steady over a few decades or generations even. My family has a business started 30 years ago that's now worth in the hundreds of millions for example, and we are ecstatic if it grows 15% per year. In the next 20 years, if we don't fail, we should have a billion dollar business. We don't take excessive risk, so there's a fairly good shot. It's a bank in the South FWIW.
It's nearly impossible to start a company and have it worth a billion dollars within a decade. But if you drop the get rich quick thinking of Silicon Valley, it's much more possible if you grow slow and steady over a few decades or generations even. My family has a business started 30 years ago that's now worth in the hundreds of millions for example, and we are ecstatic if it grows 15% per year. In the next 20 years, if we don't fail, we should have a billion dollar business. We don't take excessive risk, so there's a fairly good shot. It's a bank in the South FWIW.