Ta-daaa! From what little information I gathered on this when I first bought it, it's called "something something GET! game". The only other picture I ever found of this was on Toys n Joys' website in 2011, and I can't remember the exact name they had it listed as and I'm almost positive they don't have it even listed anymore.
From what I could gather from common sense, basically the game consists of putting the figures it comes with in the big blue...thing, and as you draw cards you put your hand in to find the figure on the card you drew.
But, you ask me, what does it come with?
ALL THIS STUFF. The game doesn't seem complex by any means, but I could have the rules of the game completely incorrect seeing as I speak no Japanese and can't find anything about this game. And yes, this is officially licensed by TOMY and all the figures in it have the official stamp.
The instructions, I think.
Here are the only painted figures that come with it, the good ol' Sinnoh starters. As far as I can tell, these TOMY figures are in completely unique poses exclusive to this game. Please feel free to let me know if these variants have been released elsewhere.
And here are all the unpainted, solid lilac-purple figures that are also included. These are ever-so-slighty smaller than normal TOMY figures, and some seem to have unique poses, but I haven't done enough research to check. The only one who is sadly broken is Weavile, who is missing its' tail. EDIT: Almost forgot Lucario, he fell off to the wayside!
Please, if you have any questions about any of this, feel free to ask! I am VERY hesitant to put it up for sale, but I'm willing to look at trades. Hope you've enjoyed reading through this post!