No it does not exist yet. This is a page devoted to pulling both private and public funding and something to wave in front of Congresscritters' eyes.
I wish Bezos, Allen, Musk, etc. weren't burning their piles of cash to see who could be first to shoot other people at the moon, but such is the world we live in.
Allen did many things with his pile of cash (though none that I know of directly involved moon trips), but no longer:
https://www.cbc.ca/radio/quirks/paul-allen-microsoft-spacesh...
Allen doesn't seem to have been going for the moon (yet), but I wish the billionaires would not spend their hoards on private rocket companies. It's a bit gross that the article you linked calls them "philanthropists" for doing it. Andrew Carnegie was a real bastard, but he funded many wonderful small-town libraries, which remain valuable community centers over 100 years later. Bill Gates took his shot at world domination, but is now using his money to solve real-world problem like malaria.
It's their money, so they can do what they want with it, but rocket companies are pure vanity. Real, cost-effective philanthropy would mean improving the perfectly acceptable planet we live on, not trying to terraform Mars.
Those problems are quite important, but I'd prefer to live in the world where space problems are among those worthy of attention.
That's a bit of an understatement of one of the worst monopolists and union-busters (even locking out employees and bringing in non-union immigrants to operate his factories) in America's history, but alright. [0]
Why didn't you mention Elon Musk and the Flint, Michigan water problem? (not to mention laptops and other donations he's made on two occasions now)
I think that's a real-world problem.
[0]: Also, he significantly contributed to the deaths of thousands through neglect of environmental standards for his own personal vacation and hunting spot. "South Fork Fishing and Hunting Club" will get you more information on him.
Giving work to immigrants. What a bastard. Everybody knows that Americans are better and more important then those dirty immigrants. They should only be allowed to get work if all white Americans already have jobs.