It's called the "Front Mission Online FPS Battle Stick", and my web searching foo has completely failed me. Or it's all sold out and unavailable.

I'll gladly send $10 to the first person to find me a place where I can buy it and get it sent to the USA or Puerto Rico successfully!
These things are not only highly collectible, there's not many left out there, and definitely none just up for sale somewhere. You're probably not gonna be finding any.
A man can dream.

Today was my second time trying to find it in awhile. Maybe others have better luck, maybe they have a weird import site that could have it.

Just thought of throwing some money at the problem.

Is it this one? With the black-and-white logo design?

It's Japanese, why not search japanese websites? Yahoo Auctions is the popular place in japan for such collector's items, but be warned, they get expensive.

Is it this? Seems to be the collector's verison, so I assume it comes with the stick?

70~80$ though, ouch.
Found it:

There's a purchase button here. You'll have to make an account to see if it will actually let you purchase it.

If that doesn't work, well, I did some additional digging:

Knowing the mecha community, you're going to have to fight tooth and nail for this one. Hope you have deep pockets.
Yes, that's the one in the youtube video.

The stick wasn't bundled, sadly.

It's sold out at "yodobashi" and at "muuz" it says discontinued product.

Thank you for trying!