Proof of what?
Sega still makes hardware. You can google that. The NU was released less than a year ago. That's on Wikipedia.
They have about 5 billion in assets, 1.3 billion cash on hand, about 850 million in debt. I suppose for comparison, they've roughly the assets as EA games. Obviously not as big as Nintendo or Activision. Certainly not Sony or MS. You can get all that from a basic investing website.
Sega blew a solid 500 mill developing and marketing the Dreamcast over the course of about two years (between start of dev in 97 and 9/9/99)- but it was state of the art and was also a very successful arcade board. I have no idea how much a modern console would cost to make, but there really isn't a reason they wouldn't be able to just slap an arcade board in a sleek black box with a DVD drive or something and throw us the old six button. They could make a new console - it just would not be worth it for them (or us probably). If we assume Sega spends 500 million develop the console and then I guess about 200 mill to market it for launch in the USA and Japan, maybe 100 mill in Europe. They'd blow through the bank account, definitely, but it is technically doable. Sega's much bigger than they were in 2000 you know.
You don't think Sega had 50 -100 mill in the bank for part 3? How broke do you think the company is? Joe's not saying they would make a return on the investment, he is saying they have the cash to do it.
Shenmue is Sega's property, not Yu's.